Dear all,

I would like to ask you to help me with the following problem that I got error.

Thanks in advance

Dear All,

I have a problem solving the attached nonlinear system of equations using shooting method.
I will be grateful if you could help me finding the solutions out.

restart; Shootlib := "C:/Shoot9"; libname := Shootlib, libname; with(Shoot);
with(plots);
N1 := 1.0; N2 := 2.0; N3 := .5; Bt := 6; Re_m := N1*Bt; gamma1 := 1;
FNS := {f(eta), fp(eta), fpp(eta), g(eta), gp(eta), m(eta), mp(eta), n(eta), np(eta), fppp(eta)};
ODE := {diff(f(eta), eta) = fp(eta), diff(fp(eta), eta) = fpp(eta), diff(fpp(eta), eta) = fppp(eta), diff(g(eta), eta) = gp(eta), diff(gp(eta), eta) = N1*(2.*g(eta)+(eta-2.*f(eta)).gp(eta)+2.*g(eta)*fp(eta)+2.*N2.N3.(m(eta).np(eta)-n(eta).mp(eta))), diff(m(eta), eta) = mp(eta), diff(mp(eta), eta) = Re_m.(m(eta)+(eta-2.*f(eta)).mp(eta)+2.*m(eta)*fp(eta)), diff(n(eta), eta) = np(eta), diff(np(eta), eta) = Re_m.(2.*n(eta)+(eta-2.*f(eta)).np(eta)+2.*N2/N3.m(eta).gp(eta)), diff(fppp(eta), eta) = N1*(3.*fpp(eta)+(eta-2.*f(eta)).fppp(eta)-2.*N2.N2.m(eta).(diff(mp(eta), eta)))};
blt := 1.0; IC := {f(0) = 0, fp(0) = 0, fpp(0) = alpha1, g(0) = 1, gp(0) = beta1, m(0) = 0, mp(0) = beta2, n(0) = 0, np(0) = beta3, fppp(0) = alpha2};
BC := {f(blt) = .5, fp(blt) = 0, g(blt) = 0, m(blt) = 1, n(blt) = 1};
infolevel[shoot] := 1;
S := shoot(ODE, IC, BC, FNS, [alpha1 = 1.425, alpha2 = .425, beta1 = -1.31, beta2 = 1.00, beta3 = 1.29]);
Error, (in isolate) cannot isolate for a function when it appears with different arguments
p := odeplot(S, [eta, fp(eta)], 0 .. 15);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p);
Error, (in plots:-display) expecting plot structure but received: p
p2 := odeplot(S, [eta, theta(eta)], 0 .. 10);
Error, (in plots/odeplot) input is not a valid dsolve/numeric solution
display(p2);
Error, (in plots:-display) expecting plot structure but received: p2

Dear All,

I am going to solve the following systems of ODEs but get the error: Newton iteration is not converging.
Could you please share your idea with me. In the case of AA=-0.2,0,0.2,0.4,...; I could get the solution.
Thank you in advance.

restart;
with(plots);
Pr := 2; Le := 2; nn := 2; Nb := .1; Nt := .1; QQ := .1; SS := .1; BB := .1; CC := .1; Ec := .1; MM := .2;AA:=-0.4;

Eq1 := diff(f(eta), `$`(eta, 3))+f(eta).(diff(f(eta), `$`(eta, 2)))-2.*nn/(nn+1).((diff(f(eta), eta))^2)-MM.(diff(f(eta), eta)) = 0; Eq2 := 1/Pr.(diff(theta(eta), `$`(eta, 2)))+f(eta).(diff(theta(eta), eta))-4.*nn/(nn+1).(diff(f(eta), eta)).theta(eta)+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2)+Ec.((diff(f(eta), `$`(eta, 2)))^2)-QQ.theta(eta) = 0;
Eq3 := diff(h(eta), `$`(eta, 2))+Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), `$`(eta, 2))) = 0;

bcs := f(0) = SS, (D(f))(0) = 1+AA.((D@@2)(f))(0), theta(0) = 1+BB.(D(theta))(0), phi(0) = 1+CC.(D(phi))(0), (D(f))(etainf) = 0, theta(etainf) = 0, phi(etainf) = 0

Error, (in dsolve/numeric/ComputeSolution) Newton iteration is not converging

Dear all,

I am trying to solve the following system of equations by using dsolve, but I get the error:  error, (in RootOf) expression independent of, _Z, could you please help me to solve it. Thank you.

restart;
Digits := 20;
with(plots);
Nr := .1; Nb := .3; Nt := .1; Rb := 0; Lb := 1; Le := 10; Pe := 1; ss := .2; aa := .1; bb := .2; cc := .3; nn := 1.5;
Eq1 := nn.(diff(f(eta), eta))^(nn-1).(diff(f(eta), `$`(eta, 2)))-(nn+1)/(2.*nn+1).eta.(diff(theta(eta), eta)-Nr.(diff(h(eta), eta))-Rb.(diff(g(eta), eta))) = 0;
Eq2 := diff(theta(eta), `$`(eta, 2))+nn/(2.*nn+1).f(eta).(diff(theta(eta), eta))+Nb.(diff(theta(eta), eta)).(diff(h(eta), eta))+Nt.((diff(theta(eta), eta))^2) = 0;
Eq3 := diff(h(eta), `$`(eta, 2))+nn/(2.*nn+1).Le.f(eta).(diff(h(eta), eta))+Nt/Nb.(diff(theta(eta), `$`(eta, 2))) = 0;
Eq4 := diff(g(eta), `$`(eta, 2))+nn/(2.*nn+1).Lb.f(eta).(diff(g(eta), eta))-Pe.((diff(g(eta), eta)).(diff(h(eta), eta))+(diff(h(eta), `$`(eta, 2))).g(eta)) = 0;
etainf := 10;
bcs := f(0) = ss/Le.(D(h))(0), theta(0) = lambda+aa.(D(theta))(0), h(0) = lambda+bb.(D(h))(0), g(0) = lambda+cc.(D(g))(0), (D(f))(etainf) = 0, theta(etainf) = 0, h(etainf) = 0, g(etainf) = 0;
dsys := {Eq1, Eq2, Eq3, Eq4, bcs};
dsol := dsolve(dsys, numeric, continuation = lambda, output = procedurelist);
Error, (in RootOf) expression independent of, _Z