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Volume 9
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Article

On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

by
Haifa Bin Jebreen
*,† and
Fairouz Tchier
†
Department of Mathematics, College of Science, King Saud University, Riyadh 11 551, Saudi Arabia
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2021, 9(1), 78; https://doi.org/10.3390/math9010078
Submission received: 23 November 2020 / Revised: 15 December 2020 / Accepted: 28 December 2020 / Published: 31 December 2020
(This article belongs to the Special Issue Recent Advances in Differential Equations and Applications)
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Abstract

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.
Keywords: interpolating scaling functions; hyperbolic equation; Galerkin method interpolating scaling functions; hyperbolic equation; Galerkin method

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MDPI and ACS Style

Bin Jebreen, H.; Tchier, F. On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method. Mathematics 2021, 9, 78. https://doi.org/10.3390/math9010078

AMA Style

Bin Jebreen H, Tchier F. On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method. Mathematics. 2021; 9(1):78. https://doi.org/10.3390/math9010078

Chicago/Turabian Style

Bin Jebreen, Haifa, and Fairouz Tchier. 2021. "On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method" Mathematics 9, no. 1: 78. https://doi.org/10.3390/math9010078

APA Style

Bin Jebreen, H., & Tchier, F. (2021). On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method. Mathematics, 9(1), 78. https://doi.org/10.3390/math9010078

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