# bvp4c for coupled interface boundary conditions

11 views (last 30 days)
Komal Goyal on 31 Jan 2023
Commented: Komal Goyal on 1 Feb 2023
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)
]

Torsten on 31 Jan 2023
Read this carefully, and you will know how to set up your problem:
Komal Goyal on 1 Feb 2023
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

### Categories

Find more on Boundary Value Problems in Help Center and File Exchange

### Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!