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Article

Fast Convergence Methods for Hyperbolic Systems of Balance Laws with Riemann Conditions

Department of Mathematics and Statistics, Faculty of Science, Jordan University of Science and Technology, Irbid 22110, Jordan
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Symmetry 2020, 12(5), 757; https://doi.org/10.3390/sym12050757
Received: 10 March 2020 / Revised: 30 March 2020 / Accepted: 9 April 2020 / Published: 6 May 2020
(This article belongs to the Special Issue Iterative Numerical Functional Analysis with Applications)
In this paper, we develop an accurate technique via the use of the Adomian decomposition method (ADM) to solve analytically a 2 × 2 systems of partial differential equation that represent balance laws of hyperbolic-elliptic type. We prove that the sequence of iteration obtained by ADM converges strongly to the exact solution by establishing a construction of fixed points. For comparison purposes, we also use the Sinc function methodology to establish a new procedure to solve numerically the same system. It is shown that approximation by Sinc function converges to the exact solution exponentially, also handles changes in type. A numerical example is presented to demonstrate the theoretical results. It is noted that the two methods show the symmetry in the approximate solution. The results obtained by both methods reveal that they are reliable and convenient for solving balance laws where the initial conditions are of the Riemann type. View Full-Text
Keywords: balance laws; sinc methods; adomian series; hyperbolic PDEs balance laws; sinc methods; adomian series; hyperbolic PDEs
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MDPI and ACS Style

Al-Khaled, K.; Rababah, N.M. Fast Convergence Methods for Hyperbolic Systems of Balance Laws with Riemann Conditions. Symmetry 2020, 12, 757. https://doi.org/10.3390/sym12050757

AMA Style

Al-Khaled K, Rababah NM. Fast Convergence Methods for Hyperbolic Systems of Balance Laws with Riemann Conditions. Symmetry. 2020; 12(5):757. https://doi.org/10.3390/sym12050757

Chicago/Turabian Style

Al-Khaled, Kamel, and Nid’a M. Rababah. 2020. "Fast Convergence Methods for Hyperbolic Systems of Balance Laws with Riemann Conditions" Symmetry 12, no. 5: 757. https://doi.org/10.3390/sym12050757

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