I have a coupled second order DE; how to solve them with boundary conditions; How to get get F1 and F2

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Nadim Mhanna
Nadim Mhanna 2017-9-27
编辑： Torsten 2017-10-2
equation 1: d^2f1/dx^2-Q/K1*F1+P/K1=0
equation 2 d^2f2/dx^2-Q/K1*F2+P/K2=0 Boundary conditions F1(0)=0 F2(l)=P F1(l-u)=F2(l-u) dF1/dx(l-u)=dF2/dx(l-u) PS All variables l, u, P,Q and K1 are known

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回答（1 个）

Torsten
Torsten 2017-9-28
Use "bvp4c" with the "multipoint boundary value problem" facility:
https://de.mathworks.com/help/matlab/ref/bvp4c.html#bt5uooc-23
https://de.mathworks.com/help/matlab/math/boundary-value-problems.html#brfhdsd-1
Best wishes
Torsten.
  2 个评论
Torsten
Torsten 2017-10-2
编辑：Torsten 2017-10-2
function dydx = f(x,y,region)
P = ...;
Q = ...;
K1 = ...;
K2 = ...;
dydx = zeros(2,1);
dydx(1) = y(2);
% The definition of dydx(2) depends on the region.
switch region
case 1 % x in [0 l-u]
dydx(2) = y(1)*Q/K1-P/K1
case 2 % x in [l-u l]
dydx(2) = y(1)*Q/K1-P/K2;
end
function res = bc(YL,YR)
P=...;
res = [YL(1,1) % y(0) = 0
YR(1,1) - YL(1,2) % Continuity of F(x) at x=l-u
YR(2,1) - YL(2,2) % Continuity of dF/dx at x=l-u
YR(1,end) - P]; % y(l) = P
You should be able to add initial conditions and call "bvp4c" following the example in my above link.
Of course, you will have to give values to the parameters used in the function routines.
Best wishes
Torsten.

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