Dear friends!
Hope you would be fine. I want to solve the following system of ODEs
restart; L := 1; with(plots); Digits := 30;
a[1] := 0; a[2] := 1; a[3] := 2; a[4] := .2; a[5] := 4; a[6] := 6;
S := 1; Pr := 6.2; a := 1; a1 := 1; a2 := 1; lambda := 1; delta := 1; Bi := 1; A := 1; B := 1;
HA := [a[1], a[2], a[3]];
Eq1 := diff(F(eta), eta, eta, eta)+a*(a1*((F(eta)+G(eta))*(diff(F(eta), eta, eta))-(diff(F(eta), eta))^2)-M1*(diff(F(eta), eta))) = 0;
Eq2 := diff(G(eta), eta, eta, eta)+a*(a1*((F(eta)+G(eta))*(diff(G(eta), eta, eta))-(diff(G(eta), eta))^2)-M1*(diff(G(eta), eta))) = 0;
Eq3 := (A+B)*(diff(H(eta), eta, eta))+a2*Pr*(F(eta)+G(eta))*(diff(H(eta), eta)) = 0;
IC1 := F(0)+G(0)=0, (D(F))(0) = 1+delta*((D@@2)(F))(0), (D(G))(0) = lambda+delta*((D@@2)(G))(0), (D(H))(0) = -Bi*(1-H(0)), (D(F))(L) = 0, (D(G))(L) = 0, H(L) = 0;
params := {B111 = .2};
associated with the above (mentioned as red) boundary conditions. The problem which I faced in first condition i.e., F(0)+G(0)=0 because its combine condition for F(eta) and G(eta) which should be use for both function. The rest part of my program is below:
for k to nops(HA) do;
P || k := plots:-odeplot(dsolve(eval({Eq1, Eq2, Eq3, IC1}, `union`(params, {M1 = .5, phi = HA[k]})), numeric), [[eta, diff(F(eta), eta)]], linestyle = [solid, solid, solid, solid][k], color = [red, green, blue, red][k], labels = [eta, f], thickness = 3) end do;
f1 := plots:-display(P || (1 .. nops(HA)));
display(f1, axes = boxed, size = [380, 310], title = "Ethylene glycol/Cu: M = 2, S = -5", titlefont = ["Arial", 12, bold]);
Please fix my problem ASAP. I also attach the maple file. Thanks in advance.
Help.mw