need help in solving 2nd order ODE using finite difference method: central scheme

d2U/dx2 = -(2*pi)^2(sin(2*pi*x)) 0<x<1;

Answer 1

[Torsten]

What are your boundary conditions ?

Best wishes

Torsten.

[deepak dalal]

Only intial condition is given 0<x<1

Let me cross check with teacher.

Thanks for your reply

[Torsten]

Since your problem is not time-dependent, initial conditions are only important for convergence. Boundary conditions are the important issue.

Best wishes

Torsten.

[deepak dalal]

boundary condition: u = 0 at x = 0 and x = 1

thanks

[Torsten]

Then you will have to solve the linear system of equations

u(1)=0
(u(i+1)-2*u(i)+u(i-1))/(dh)^2=-(2*pi)^2*sin(2*pi*(i-1)*dh) (2<=i<=n-1)
u(n)=0

with

dh=1/(n-1)

See whether MATLAB supplies a solver for tridiagonal systems of linear equations.

Best wishes

Torsten.

[deepak dalal]

I can not use any solver tool. I have to write a matlab code for getting solution. do you have code for similar boundary layer problem.

[Torsten]

The linear system has the form

A*u=b

Set up A and b and solve for u using u=A\b.

Best wishes

Torsten.