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## Nonlinear Finite Difference Method

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The Finite Difference Method is employed for solving a nonlinear boundary value problem.

Updated

The function nonlinearBVP_FDM .m is an implementation of the
nonlinear finite difference method for the general nonlinear
boundary-value problem ---------------------------------------------
y''=f(x,y,y'), for a<x<b where y(a)=alpha and y(b)=beta.
----------------------------------------------------------------------------
The interval [a,b] is divided into (N+1) equal subintervals
with endpoints at x(i)=a+i*h for i=0,1,2,...,N+1.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Remarks:
The function f should be defined as an m-file.
There is NO need for partial derivatives of f
See given example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

Example
Solve the nonlinear boundary value problem
y''=(1/8)*(32+2x^3-yy'), for 1<x<3, where y(1)=17 and y(3)=43/3
Step 1...
Create the function f as a separate m-file and save it in the
current working directory.
function f = f(x,y,yp)
f = (1/8)*(32+2*x^3-y*yp); %Note that yp=y'
Step 2...
In the command window type
>> Y = nonlinearBVP_FDM(1,3,17,43/3);
Note that Y(:,1) represents x and Y(:,2) is vector y(x)
The solution is then plotted in a new figure
If the exact solution is given, plot it for comparison
>> yexact = (Y(:,1)).^2+16./Y(:,1); plot(Y(:,1),yexact,'c')

Chen Yu-Lin

Hongwei Guo

BGU

Mohsin Shah

### Mohsin Shah (view profile)

Hi
im looking for any one who help me writing Matlab code pulse propagation in optical fiber using the nonlinear schrodinger equation by the help of FDTD method. please reply if there is anyone

so far

### so far (view profile)

Hi all..
I'm looking for anyone who can rewrite(revise) my matlab program to solve pdes(continuity,momentum,energy)in three Dimensions...please I need serious help...
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##### MATLAB Release
MATLAB 7.7 (R2008b)