Hello

Hope everything going fine with you. I am facing problem to fine the exact (numerical) solution of the attached system of linear PDEs associated with BSc and ICs. I tried to solve it without BCs and ICs, with BCs and with ICs also all the times I failed. Please solve it either general, with ICs or BCs. You can try to solve it numrically. In attached file H(t) represent the unit step function. I am waiting your positive response.

PDEs_solve.mw 

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hello!

Hope everyone good. I am facing problem to define a loop. Actually I want to solve the attached file for different values of H like H=[100,125,140,160] for this I don't know how to tackle it. My program do working on single value of H. Please solve my problem as soon as possible. I am waiting your positive response. 

Help.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Hello! I am facing the problem to making the grahp of system of ODEs in the attached file from eta=-1..1. Please see the attachment and fixed it. I will be waiting your positive response.

new_graph_exact.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Email: muhammadusman@pku.edu.cn

Mob #: 0086-13001903838

Dears;

Hope everyone is fine. I am try to find the numerical solutions of system of nonlinear algabric equation via newton's raphson method in the attached file but failed. Please see the attachment and try to correct. You can solve it least square method if possible. I am waiting your positive response. 

Help_in_Newton.mw

With my best regards and sincerely.

Muhammad Usman

School of Mathematical Sciences 
Peking University, Beijing, China

Email: muhammadusman@pku.edu.cn

Aslam o Alikum!

Hope everyone going fine with sound health I want to make the graph of following system of ODEs

Eq1 := diff(F(eta), eta, eta, eta, eta)-M*(eta*(diff(F(eta), eta, eta, eta))+3*(diff(F(eta), eta, eta))+(diff(F(eta), eta))*(diff(F(eta), eta, eta))-F(eta)*(diff(F(eta), eta, eta, eta)))-Ha^2*(diff(F(eta), eta, eta));
Eq2 := diff(G(eta), eta, eta)+Pr*M*(F(eta)*(diff(G(eta), eta))-eta*(diff(G(eta), eta)))+Pr*Ec*(diff(F(eta), eta, eta))^2+Nb*(diff(H(eta), eta))+diff(G(eta), eta)+Nt*(diff(G(eta), eta))^2;
Eq3 := diff(H(eta), eta, eta)+M*Sc*(F(eta)*(diff(H(eta), eta))-eta*(diff(H(eta), eta)))+Nt*(diff(F(eta), eta, eta))/Nb;
 

using the BC's

IC1 := F(0) = 0, ((D@@2)(F))(0) = 0, (D(G))(0) = 0, (D(H))(0) = 0;
     F(0) = 0, @@(D, 2)(F)(0) = 0, D(G)(0) = 0, D(H)(0) = 0
IC2 := F(1) = 1, (D(F))(1) = 0, G(1) = 1, H(1) = 1;
 

for Ec := .1; Nt := .1; Nb := .1; Sc := .5; Pr := 10; M := .5; and different values of Ha like Ha:=0, Ha:=2, Ha:=4, Ha:=6 and Ha:=8 in one coordinate. 

I am waiting your positive response.