求解时变偏微分方程的切比雪夫展开法

E. Elbarbary
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引用次数: 0

摘要

提出了求解抛物型方程和Burgers方程的Chebyshev展开方法。空间导数用切比雪夫多项式逼近,时间导数用有限差分格式处理。在时间方向上采用合适的外推方案,提高了结果的精度。切比雪夫展开法是基于对其任意阶导数的切比雪夫多项式使用显式公式。此外,这个公式还用于将微分方程中出现的导数的阶数等同于微分方程的阶数。采用逐次积分的方法,得到了展开式系数的代数系统。最后,通过数值算例验证了该方法的可行性。版权所有©2007 John Wiley & Sons, Ltd
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Chebyshev expansion method for solving the time‐dependent partial differential equations
A Chebyshev expansion method for the parabolic and Burgers equations is developed. The spatial derivatives are approximated by the Chebyshev polynomials and the time derivative is treated by a finite-difference scheme. The accuracy of the resultant is modified by using suitable extrapolation scheme in the time direction. The Chebyshev expansion method is based on using an explicit formula for the Chebyshev polynomials in terms of arbitrary order of their derivatives. In addition, this formula is used in equating the order of derivatives appearing in the differential equation to the order of differential equation. The successive integration is used to obtain an algebraic system in the expansion coefficients. Finally, numerical examples are studied to demonstrate the viability of this method. Copyright © 2007 John Wiley & Sons, Ltd.
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