MATLAB 1D 2nd-Order nonlinear differential eqn in Matlab

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Hi all,

I am more into physics than maths and I need you guys to please help me out. Also I am new to programming in MATLAB. I have done some but still I consider myself a novice. I need to solve the problem in MATLAB.

So here is the problem.Its a 2 point BVP(boundary value problem) along a straight line ,say along x-axis , from -L to +L.


A*N''=B+(C*N)+(D*N^2)+f(N)


[prime denotes differentiation w.r.t x, N~N(x) , f(N) is a simple function of N, say log(N), All constants are known]

Now I need to solve this BVP for the following boundary conditions:N(-L)=B1 and N(L)=B2, Both B1 and B2 are also known.

The problem is that this particular equation needs to be solved using the "Relaxation Method" and Runge-Kutta/ Shooting method's are not considered suitable traditionally for this diffusion like problem.

Can any body suggest me a code for this problem in Matlab. I haven't seen any function in MATLAB capable of solving NL BVP.

Please help.

Sincerely,

JAM
 

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