The Discrete Orthogonal Polynomial Least Squares Method for Approximation and Solving Partial Differential Equations
Year: 2008
Communications in Computational Physics, Vol. 3 (2008), Iss. 3 : pp. 734–758
Abstract
We investigate numerical approximations based on polynomials that are orthogonal with respect to a weighted discrete inner product and develop an algorithm for solving time dependent differential equations. We focus on the family of super Gaussian weight functions and derive a criterion for the choice of parameters that provides good accuracy and stability for the time evolution of partial differential equations. Our results show that this approach circumvents the problems related to the Runge phenomenon on equally spaced nodes and provides high accuracy in space. For time stability, small corrections near the ends of the interval are computed using local polynomial interpolation. Several numerical experiments illustrate the performance of the method.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-CiCP-7873
Communications in Computational Physics, Vol. 3 (2008), Iss. 3 : pp. 734–758
Published online: 2008-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 25