bvp4c for coupled interface boundary conditions

Question

Komal Goyal 2023-1-31

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1903885-bvp4c-for-coupled-interface-boundary-conditions

评论： Komal Goyal 2023-2-1

BVP4c.pdf

Here I am trying to solve a system of ODE with coupled boundary conditions, but got stucked. I dont know how to define coupled boundary condition in Matlab. Can anybody please help me. If any other information is required please let me know. Moreover, one PDF file is also attached there with name bvp4c with the complete details of the ODE and respective boundary conditions.

function pp(solver)
infinity =1;
maxinfinity=infinity;
pp1=infinity;
pp2=maxinfinity;
%CONSTANTS
%--------------------------------------------------------------------------
p=0.01;
e=0.783;
H=1;
M=1;
a=1.92;
%--------------------------------------------------------------------------
solver = 'bvp4c';
bvpsolver = fcnchk(solver);
infinity = pp1;
maxinfinity = pp2;
Mva=[0.5 1 1.5 2];
colors = ['k','m','r','b']; 
for j = 1:4
    Le=Mva(j);
    for d=Mva(j)
        solinit = bvpinit(linspace(0,infinity,45),[1 1 1 0 1 0 1 0 0 1 1 1 1 1 1 1]);
        sol = bvpsolver(@fsode,@fsbc,solinit);
        eta = sol.x;
        f = sol.y;
        solinit = bvpinit(linspace(0,0.5,100),[0.001 0 0 0]);
        sol = bvp4c(@pp2_ode,@pp2_bc,solinit,options);
        
        x = sol.x;
        y1 = sol.y(1,:); 
        y2 = sol.y(2,:);
        y3 = sol.y(3,:);
        y4 = sol.y(4,:);
        
        figure(5)
        plot(real(y(1,:)+p*exp(1i*t)*y(3,:)),eta,colors(j),'LineWidth',2)
        plot(real(y(5,:)+p*exp(1i*t)*y(7,:)),eta,colors(j),'LineWidth',2)
        hold on
        
        
        %--------------------------------------------------------------------------
        function dydx = pp2_ode(x,y)
            
            dydx = [y(2)
                (((M^2)*y(1))-((H)^2))
                y(4)
                (((M^2)+(i*((H)^2)))*y(3))-((H)^2)
                y(6)
                -a*((H)^2)
                y(8)
                ((i*a*(H)^2)*y(7))/e-(a*((H)^2))];
        end
        %--------------------------------------------------------------------------
        function res = pp2_bc(ya,yb)
            res = [ ya(1)
                ]

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Answer 1

Torsten 2023-1-31

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链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/1903885-bvp4c-for-coupled-interface-boundary-conditions#answer_1160385

Read this carefully, and you will know how to set up your problem:

https://de.mathworks.com/help/matlab/math/solve-bvp-with-multiple-boundary-conditions.html

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Komal Goyal 2023-2-1

Thank you @Torsten for you suggestion. After reading that, I was trying to write code for my ODEs, but it was showing some error. Can you please check that once, Just now I uploded that as my question.

Once again thank you

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