Chebyshev collocation method
 

Dear all,

I would like to use Chebyshev collocation method to compute the derivative of function sin(x). Collocation point is taken the form of Gauss-Lobatto. When the number of grid points is small. For example, 50, 100, 200and 300 on interval [0, 2*pi], the accuracy is very high. But with the grid number increasing, the accuracy is lower. Does anybody has experience with Chebyshev collocation method? Could you help me?

Thanks very much!

Re: Chebyshev collocation method
 

Hello,

When then grid number gets too high, machine error dominates the results. You might want to perform the computations in a higher precision. You might also want to consider dividing the domain into multiple sub-domains to capture features of interest. Why do you need to have more that 200 points for the derivative of sin? I assume that you eventually wish to model a more complex problem.

Much success.

Regards, Patrick Hanley,Ph.D. http://www.hanleyinnovations.com Aerodynamics Software for the PC.

Re: Chebyshev collocation method
 

Chebyshev polynomial is defined on interval [-1,1]. Problems on other finite intervals may be mapped onto the standard interval. Mapping is often useful in improving the accuracy of a Chebyshev expansion. If number of grid pionts is very large, the nodes may be compressed together somewhere. So you should choose an appropriate mapping which clusters points as desired.

Good luck!

Chebyshev Collocation method
 

I face a problem. How can we solve a coupled differential eigen value problem with chebyshev collocation method,without using the conventional gauss-lobatto quadrature points, and use of differentiation matrices.

I have a paper where they used chebyshev expansion of the variable uptil N+N' where N is the truncation parameter of the series and N' is the the number of boundary conditions incorporated.It will be nice,if i can get through this problem,which i am stuck up to for a week or so...

i have incorporated the pages, for you to refer...

thanks in advance .