Approximation of Multivariate Functions and Evaluation of Particular Solutions Using Chebyshev Polynomial and Trigonometric Basis Functions

Document Type

Article

Publication Date

9-24-2006

Department

Mathematics

School

Mathematics and Natural Sciences

Abstract

A two-stage numerical procedure using Chebyshev polynomials and trigonometric functions is proposed to approximate the source term of a given partial differential equation. The purpose of such numerical schemes is crucial for the evaluation of particular solutions of a large class of partial differential equations. Our proposed scheme provides a highly efficient and accurate approximation of multivariate functions and particular solution of certain partial differential equations simultaneously. Numerical results on the approximation of eight two-dimensional test functions and their derivatives are given. To demonstrate that the scheme for the approximation of functions can be easily extended to evaluate the particular solution of certain partial differential equations, we solve a modified Helmholtz equation. Near machine precision can be achieved for all these test problems. Copyright (c) 2006 John Wiley & Sons, Ltd.

Publication Title

International Journal for Numerical Methods in Engineering

Volume

67

Issue

13

First Page

1811

Last Page

1829

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