MATLAB: How do i use BVP4C for these kind of coupled odes

boundary value problembvp4cbvpinitMATLABodeode45

The equations are coupled

C1 p(x) + C2 dp(x)/dx + C3 u(x) + C4 du(x)/dx = 0

C5 p(x) + C6 dp(x)/dx + C7 u(x) + C8 du(x)/dx = 0

I want to give two boundary conditions, one at each end. (thus cannot use ode45).

I have seen how bvp4c works with higher order odes with boundary value problems. the difficulty here is that the first order coupled equations both contain the first derivatives of each terms. Any help is appreciated. Thanks

Best Answer

Can you solve

C2*a + C4*b = -C1*p(x) - C3*u(x)
C6*a + C8*b = -C5*p(x) - C7*u(x)

for a and b ?

If this is the case, then

a = dp(x)/dx , b = du(x)/dx.

Best wishes

Torsten.

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MATLAB: How do i use boundary conditions to find variables in an equation

if you let Lp=constant and make changes in

soln = solve(u,eqns,vars);

soln = solve(eqns);

you will get a structure soln and in the command window you can access the value for each variable by soln.[variable], for example soln.c1

MATLAB: Solve symbol four equations for c1 c2 c3 c4

Thanks, I solve it,

clc
clear
syms a b x y c1 c2 c3 c4 T1 T2 T3 T4  
T=c1+c2*x+c3*y+c4*x*y;
%%
r1=c1+c2*a+c3*b+c4*a*b-T1;
r2=c1-c2*a+c3*b-c4*a*b-T2;
r3=c1-c2*a-c3*b+c4*a*b-T3;
r4=c1+c2*a-c3*b-c4*a*b-T4;
%%Find C1 and C4
p13=r1+r3;
p24=r2+r4;
n1=solve(p13==0,c1);
n2=solve(p24==0,c1);
C4=solve(n1==n2,c4)
w1=solve(p13==0,c4);
w2=solve(p24==0,c4);
C1=solve(w1==w2,c1)
r1=subs(r1,c1,C1);
r1=subs(r1,c4,C4);
r2=subs(r2,c1,C1);
r2=subs(r2,c4,C4);
r3=subs(r3,c1,C1);
r3=subs(r3,c4,C4);
r4=subs(r4,c1,C1);
r4=subs(r4,c4,C4);
%%Find C3
q12=r1+r2;
q34=r3+r4;
C3=solve(q12==0,c3)
r1=subs(r1,c3,C3);
r2=subs(r2,c3,C3);
r3=subs(r3,c3,C3);
r4=subs(r4,c3,C3);
%% find C2
C2=solve(r1==0,c2)
r1=subs(r1,c2,C2);
r2=subs(r2,c2,C2);
r3=subs(r3,c2,C2);
r4=subs(r4,c2,C2);
C1
C2
C3
C4

Best Answer

Related Solutions

MATLAB: How do i use boundary conditions to find variables in an equation

MATLAB: Solve symbol four equations for c1 c2 c3 c4

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