Error analysis of the Chebyshev collocation method for linear second-order partial differential equations

Abstract

The purpose of this study is to apply the Chebyshev collocation method to linear second-order partial differential equations (PDEs) under the most general conditions. The method is given with a priori error estimate which is obtained by polynomial interpolation. The residual correction procedure is modified to the problem so that the absolute error may be estimated. Finally, the effectiveness of the method is illustrated in several numerical experiments such as Laplace and Poisson equations. Numerical results are overlapped with the theoretical results.

Keywords:

• partial differential equations
• Chebyshev collocation method
• Chebyshev polynomial solutions
• error analysis of collocation methods
• residual correction procedure

2010 AMS Subject Classifications::

• 35G05
• 65M70