Example 5.7 Semianalytical Method for PDEs wtih Known Initial Profiles 

> restart;
 

> with(linalg):with(plots):
 

> ge:=diff(u(x,t),t)=Ds*diff(u(x,t),x$2);
 

diff(u(x, t), t) = `*`(Ds, `*`(diff(diff(u(x, t), x), x))) (1)
 

> bc1:=diff(u(x,t),x);
 

diff(u(x, t), x) (2)
 

> bc2:=u(x,t);
 

u(x, t) (3)
 

> IC:=u(x,0)=cos(Pi*x/2/L);
 

u(x, 0) = cos(`+`(`/`(`*`(`/`(1, 2), `*`(Pi, `*`(x))), `*`(L)))) (4)
 

> L:=0.02;
 

0.2e-1 (5)
 

> Ds:=2e-5;
 

0.2e-4 (6)
 

> N:=10;
 

10 (7)
 

> dydxf:=1/2*(-u[2](t)-3*u[0](t)+4*u[1](t))/h;
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(`-`(u[2](t)), `-`(`*`(3, `*`(u[0](t)))), `*`(4, `*`(u[1](t)))))), `*`(h))) (8)
 

> dydxb:=1/2*(u[N-1](t)+3*u[N+1](t)-4*u[N](t))/h;
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(u[9](t), `*`(3, `*`(u[11](t))), `-`(`*`(4, `*`(u[10](t))))))), `*`(h))) (9)
 

> dydx:=1/2/h*(u[m+1](t)-u[m-1](t));
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(u[`+`(m, 1)](t), `-`(u[`+`(m, `-`(1))](t))))), `*`(h))) (10)
 

> d2ydx2:=1/h^2*(u[m-1](t)-2*u[m](t)+u[m+1](t));
 

`/`(`*`(`+`(u[`+`(m, `-`(1))](t), `-`(`*`(2, `*`(u[m](t)))), u[`+`(m, 1)](t))), `*`(`^`(h, 2))) (11)
 

> bc1:=subs(diff(u(x,t),x)=dydxf,u(x,t)=u[0](t),x=0,bc1);
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(`-`(u[2](t)), `-`(`*`(3, `*`(u[0](t)))), `*`(4, `*`(u[1](t)))))), `*`(h))) (12)
 

> bc2:=subs(diff(u(x,t),x)=dydxb,u(x,t)=u[N+1](t),x=1,bc2);
 

u[11](t) (13)
 

> eq[0]:=bc1;
 

`+`(`/`(`*`(`/`(1, 2), `*`(`+`(`-`(u[2](t)), `-`(`*`(3, `*`(u[0](t)))), `*`(4, `*`(u[1](t)))))), `*`(h))) (14)
 

> eq[N+1]:=bc2;
 

u[11](t) (15)
 

> for i from 1 to N do eq[i]:=diff(u[i](t),t)= subs(diff(u(x,t),x$2) = subs(m=i,d2ydx2),diff(u(x,t),x) = subs(m=i,dydx),u(x,t)=u[i](t),x=i*h,rhs(ge));od;
 

 

 

 

 

 

 

 

 

 

diff(u[1](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[0](t), `-`(`*`(2, `*`(u[1](t)))), u[2](t)))), `*`(`^`(h, 2))))
diff(u[2](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h, 2))))
diff(u[3](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[2](t), `-`(`*`(2, `*`(u[3](t)))), u[4](t)))), `*`(`^`(h, 2))))
diff(u[4](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[3](t), `-`(`*`(2, `*`(u[4](t)))), u[5](t)))), `*`(`^`(h, 2))))
diff(u[5](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[4](t), `-`(`*`(2, `*`(u[5](t)))), u[6](t)))), `*`(`^`(h, 2))))
diff(u[6](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[5](t), `-`(`*`(2, `*`(u[6](t)))), u[7](t)))), `*`(`^`(h, 2))))
diff(u[7](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[6](t), `-`(`*`(2, `*`(u[7](t)))), u[8](t)))), `*`(`^`(h, 2))))
diff(u[8](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[7](t), `-`(`*`(2, `*`(u[8](t)))), u[9](t)))), `*`(`^`(h, 2))))
diff(u[9](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[8](t), `-`(`*`(2, `*`(u[9](t)))), u[10](t)))), `*`(`^`(h, 2))))
diff(u[10](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[9](t), `-`(`*`(2, `*`(u[10](t)))), u[11](t)))), `*`(`^`(h, 2)))) (16)
 

> u[0](t):=(solve(eq[0],u[0](t)));
 

`+`(`-`(`*`(`/`(1, 3), `*`(u[2](t)))), `*`(`/`(4, 3), `*`(u[1](t)))) (17)
 

> u[N+1](t):=solve(eq[N+1],u[N+1](t));
 

0 (18)
 

> for i from 1 to N do eq[i]:=eval(eq[i]);od;
 

 

 

 

 

 

 

 

 

 

diff(u[1](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(`*`(`/`(2, 3), `*`(u[2](t))), `-`(`*`(`/`(2, 3), `*`(u[1](t))))))), `*`(`^`(h, 2))))
diff(u[2](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h, 2))))
diff(u[3](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[2](t), `-`(`*`(2, `*`(u[3](t)))), u[4](t)))), `*`(`^`(h, 2))))
diff(u[4](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[3](t), `-`(`*`(2, `*`(u[4](t)))), u[5](t)))), `*`(`^`(h, 2))))
diff(u[5](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[4](t), `-`(`*`(2, `*`(u[5](t)))), u[6](t)))), `*`(`^`(h, 2))))
diff(u[6](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[5](t), `-`(`*`(2, `*`(u[6](t)))), u[7](t)))), `*`(`^`(h, 2))))
diff(u[7](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[6](t), `-`(`*`(2, `*`(u[7](t)))), u[8](t)))), `*`(`^`(h, 2))))
diff(u[8](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[7](t), `-`(`*`(2, `*`(u[8](t)))), u[9](t)))), `*`(`^`(h, 2))))
diff(u[9](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[8](t), `-`(`*`(2, `*`(u[9](t)))), u[10](t)))), `*`(`^`(h, 2))))
diff(u[10](t), t) = `+`(`/`(`*`(0.2e-4, `*`(`+`(u[9](t), `-`(`*`(2, `*`(u[10](t))))))), `*`(`^`(h, 2)))) (19)
 

> eqs:=[seq(rhs(eq[j]),j=1..N)];
 

[`+`(`/`(`*`(0.2e-4, `*`(`+`(`*`(`/`(2, 3), `*`(u[2](t))), `-`(`*`(`/`(2, 3), `*`(u[1](t))))))), `*`(`^`(h, 2)))), `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h...
[`+`(`/`(`*`(0.2e-4, `*`(`+`(`*`(`/`(2, 3), `*`(u[2](t))), `-`(`*`(`/`(2, 3), `*`(u[1](t))))))), `*`(`^`(h, 2)))), `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h...
[`+`(`/`(`*`(0.2e-4, `*`(`+`(`*`(`/`(2, 3), `*`(u[2](t))), `-`(`*`(`/`(2, 3), `*`(u[1](t))))))), `*`(`^`(h, 2)))), `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h...
[`+`(`/`(`*`(0.2e-4, `*`(`+`(`*`(`/`(2, 3), `*`(u[2](t))), `-`(`*`(`/`(2, 3), `*`(u[1](t))))))), `*`(`^`(h, 2)))), `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h...
[`+`(`/`(`*`(0.2e-4, `*`(`+`(`*`(`/`(2, 3), `*`(u[2](t))), `-`(`*`(`/`(2, 3), `*`(u[1](t))))))), `*`(`^`(h, 2)))), `+`(`/`(`*`(0.2e-4, `*`(`+`(u[1](t), `-`(`*`(2, `*`(u[2](t)))), u[3](t)))), `*`(`^`(h...
(20)
 

> Y:=[seq(u[i](t),i=1..N)];
 

[u[1](t), u[2](t), u[3](t), u[4](t), u[5](t), u[6](t), u[7](t), u[8](t), u[9](t), u[10](t)] (21)
 

> A:=genmatrix(eqs,Y);
 

array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = `+`(`/`(`*`(0.2e-4), `*`(`^`(h, 2)))), ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = `+`(`/`(`*`(0....
(22)
 

> h:=eval(L/(N+1));
 

0.1818181818e-2 (23)
 

> A:=map(eval,A);
 

array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0, ( 6, 2 ) = 0, ( 8, 2 ) = 0, ( 4, 7 ) = 0, ( 2, 5 ) = 0, ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0, ( 5, 7 ) = 0, ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0, ( 8, 10 ) = 0...
(24)
 

> if N > 4 then A:=map(evalf,A);end:
 

> evalm(A);
 

array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
array( 1 .. 10, 1 .. 10, [( 3, 5 ) = 0., ( 6, 2 ) = 0., ( 8, 2 ) = 0., ( 4, 7 ) = 0., ( 2, 5 ) = 0., ( 7, 8 ) = 6.050000002, ( 10, 3 ) = 0., ( 5, 7 ) = 0., ( 9, 8 ) = 6.050000002, ( 3, 6 ) = 0., ( 8, ...
(25)
 

> mat:=exponential(A,t):
 

> mat:=map(evalf,mat):
 

> Y0:=matrix(N,1):for i from 1 to N do Y0[i,1]:=evalf(subs(x=i*h,rhs(IC)));od:evalm(Y0);
 

array( 1 .. 10, 1 .. 1, [( 5, 1 ) = .7557495745, ( 4, 1 ) = .8412535328, ( 10, 1 ) = .1423148380, ( 9, 1 ) = .2817325565, ( 7, 1 ) = .5406408173, ( 2, 1 ) = .9594929736, ( 1, 1 ) = .9898214419, ( 6, 1... (26)
 

> Y:=evalm(mat&*Y0):
 

> Y:=map(simplify,Y);
 

array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
array( 1 .. 10, 1 .. 1, [( 5, 1 ) = `+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`...
(27)
 

> for i from 1 to N do u[i](t):=evalf((Y[i,1]));od:
 

> for i from 0 to N+1 do u[i](t):=eval(u[i](t));od;
 

 

 

 

 

 

 

 

 

 

 

 

`+`(`*`(0.9593000000e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.76666667e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.1007306667e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))...
`+`(`*`(0.9593000000e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.76666667e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.1007306667e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))...
`+`(`*`(0.9593000000e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.76666667e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.1007306667e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))...
`+`(`*`(0.9593000000e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.76666667e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.1007306667e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))...
`+`(`*`(0.3874e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.26083e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.43738e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`...
`+`(`*`(0.3874e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.26083e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.43738e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`...
`+`(`*`(0.3874e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.26083e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.43738e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`...
`+`(`*`(0.3874e-7, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.26083e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.43738e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`...
`+`(`-`(`*`(0.13283e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.106632e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.127240e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t...
`+`(`-`(`*`(0.13283e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.106632e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.127240e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t...
`+`(`-`(`*`(0.13283e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.106632e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.127240e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t...
`+`(`-`(`*`(0.13283e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.106632e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.127240e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t...
`+`(`*`(0.28098e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.3463e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.14775e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`(0.67...
`+`(`*`(0.28098e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.3463e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.14775e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`(0.67...
`+`(`*`(0.28098e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.3463e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.14775e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`(0.67...
`+`(`*`(0.28098e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.3463e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `*`(0.14775e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `*`(0.67...
`+`(`-`(`*`(0.30377e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.12950e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.42666e-7, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))...
`+`(`-`(`*`(0.30377e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.12950e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.42666e-7, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))...
`+`(`-`(`*`(0.30377e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.12950e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.42666e-7, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))...
`+`(`-`(`*`(0.30377e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.12950e-5, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.42666e-7, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))...
`+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))), `-`...
`+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))), `-`...
`+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))), `-`...
`+`(`*`(0.41045e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `*`(0.7714e-8, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.89017e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))), `-`...
`+`(`-`(`*`(0.3838e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.28438e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.164389e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`-`(`*`(0.3838e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.28438e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.164389e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`-`(`*`(0.3838e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.28438e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.164389e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`-`(`*`(0.3838e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `-`(`*`(0.28438e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.164389e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`*`(0.378327e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.8381e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.65485e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))...
`+`(`*`(0.378327e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.8381e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.65485e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))...
`+`(`*`(0.378327e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.8381e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.65485e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))...
`+`(`*`(0.378327e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.8381e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `-`(`*`(0.65485e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t)))))))...
`+`(`-`(`*`(0.33037e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.6151e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.48967e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))))...
`+`(`-`(`*`(0.33037e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.6151e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.48967e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))))...
`+`(`-`(`*`(0.33037e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.6151e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.48967e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))))...
`+`(`-`(`*`(0.33037e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.6151e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.48967e-6, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))))...
`+`(`*`(0.21380e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.9872e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.151806e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `-...
`+`(`*`(0.21380e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.9872e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.151806e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `-...
`+`(`*`(0.21380e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.9872e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.151806e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `-...
`+`(`*`(0.21380e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t))))))), `-`(`*`(0.9872e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t)))))))), `*`(0.151806e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))), `-...
`+`(`-`(`*`(0.13112e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.41057e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.117061e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`-`(`*`(0.13112e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.41057e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.117061e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`-`(`*`(0.13112e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.41057e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.117061e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
`+`(`-`(`*`(0.13112e-6, `*`(exp(`+`(`-`(`*`(23.63625745, `*`(t)))))))), `*`(0.41057e-6, `*`(exp(`+`(`-`(`*`(21.99944289, `*`(t))))))), `-`(`*`(0.117061e-5, `*`(exp(`+`(`-`(`*`(19.44730116, `*`(t))))))...
0 (28)
 

> tf:=20;
 

20 (29)
 

Set the color list: 

> setcolors(["Red", "Blue", "LimeGreen", "Goldenrod", "maroon", "DarkTurquoise", "coral", "aquamarine", "magenta", "khaki",  "sienna", "orange", "yellow", "gray"]);
 

[ (30)
 

> pp:=plot([seq(u[i](t),i=0..N+1)],t=0..tf,thickness=3);
 

PLOT(CURVES([[0., .999930945945673776], [.435943083333333314, .947530222103962982], [.815254829166666694, .904218093252551869], [1.24183055833333334, .857881695815127854], [1.67123390833333362, .81364... (31)
 

Plot the texts: 

> arw:=arrow(<6.0,0.55>,<-5.0,-0.57>,width=[1/1000,relative=true],head_width=[1/50,relative=false],head_length=[1/5,relative=false]):
pt:=textplot([[11,0.6,typeset("Follow the arrow: ",u[0],"(t), ..., ",u[N+1],"(t).")]]):
 

> display([pp,pt,arw],title="Figure Exp. 5.25.",axes=boxed,labels=[t,"u"]);
 

Plot_2d
 

> tf:=20;
 

20 (32)
 

> M:=30;
 

30 (33)
 

> T1:=[seq(tf*i/M,i=0..M)];
 

[0, `/`(2, 3), `/`(4, 3), 2, `/`(8, 3), `/`(10, 3), 4, `/`(14, 3), `/`(16, 3), 6, `/`(20, 3), `/`(22, 3), 8, `/`(26, 3), `/`(28, 3), 10, `/`(32, 3), `/`(34, 3), 12, `/`(38, 3), `/`(40, 3), 14, `/`(44,...
[0, `/`(2, 3), `/`(4, 3), 2, `/`(8, 3), `/`(10, 3), 4, `/`(14, 3), `/`(16, 3), 6, `/`(20, 3), `/`(22, 3), 8, `/`(26, 3), `/`(28, 3), 10, `/`(32, 3), `/`(34, 3), 12, `/`(38, 3), `/`(40, 3), 14, `/`(44,...
(34)
 

> PP:=matrix(N+2,M+1);
 

array( 1 .. 12, 1 .. 31, [ ] ) (35)
 

> for i from 1 to N+2 do PP[i,1]:=evalf(subs(x=(i-1)*h,rhs(IC)));od:
 

> for i from 1 to N+2 do for j from 2 to M+1 do PP[i,j]:=evalf(subs(t=T1[j],u[i-1](t)));od;od:
 

> plotdata:=[seq([ seq([(i-1)*h,T1[j],PP[i,j]], i=1..N+2)], j=1..M+1)]:
 

> surfdata(plotdata,axes=boxed,title="Figure 5.26.",labels=[x,t,u],orientation=[45,60]);
 

Plot
 

>