Numerical solution of PDE using two dimensional chebyshev wavelet collocation method

Abstract

In this current work, we investigate a new computational scheme to solve a system of Partial Differential Equations. To handle this method, we initially construct a Two Dimensional Chebyshev wavelet which is used to transform the PDE’s to a linear system of algebraic equations. We approximate the obtained algebraic equations using collocation method. This algorithm can be easily implemented to solve PDE with boundary conditions. We illustrate with examples to analyze the convergence using this Two Dimensional Chebyshev collocation method. Finally, we show the validity, efficiency and applicability of this new technique with some Numerical Examples.