A Two-Dimensional Chebyshev Wavelet Method for Solving Partial Di erential Equations

Abstract

In this paper, we introduce a two-dimensional Chebyshev wavelet method (TCWM) for solving partial di erential equations (PDEs) in L2(R) space. In this method, the spatial variables appearing in the PDE each has its own kernel, as well as wavelet coecient for approxi- mating the unknown solution of the equation. The approximated solu- tion of the equation is fast and has higher number of vanishing moments as compared to the Chebyshev wavelet method with only one wavelet coecient for two or more separated kernels for the variables appearing in the PDE.