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Axioms 2018, 7(4), 70; https://doi.org/10.3390/axioms7040070

A New Efficient Method for the Numerical Solution of Linear Time-Dependent Partial Differential Equations

Department of Applied Mathematics, Faculty of Mathematics, Yazd University, P. O. Box 89195-741, Yazd, Iran
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Received: 5 August 2018 / Revised: 21 September 2018 / Accepted: 28 September 2018 / Published: 1 October 2018
(This article belongs to the Special Issue New Trends in Differential and Difference Equations and Applications)
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Abstract

This paper presents a new efficient method for the numerical solution of a linear time-dependent partial differential equation. The proposed technique includes the collocation method with Legendre wavelets for spatial discretization and the three-step Taylor method for time discretization. This procedure is third-order accurate in time. A comparative study between the proposed method and the one-step wavelet collocation method is provided. In order to verify the stability of these methods, asymptotic stability analysis is employed. Numerical illustrations are investigated to show the reliability and efficiency of the proposed method. An important property of the presented method is that unlike the one-step wavelet collocation method, it is not necessary to choose a small time step to achieve stability. View Full-Text
Keywords: Legendre wavelets; collocation method; three-step Taylor method; asymptotic stability; time-dependent partial differential equations Legendre wavelets; collocation method; three-step Taylor method; asymptotic stability; time-dependent partial differential equations
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Torabi, M.; Hosseini, M.-M. A New Efficient Method for the Numerical Solution of Linear Time-Dependent Partial Differential Equations. Axioms 2018, 7, 70.

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