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The Space–Time Kernel-Based Numerical Method for Burgers’ Equations

Department of Basic Sciences, University of Engineering and Technology, Peshawar 25000, Pakistan
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Mathematics 2018, 6(10), 212; https://doi.org/10.3390/math6100212
Received: 26 September 2018 / Revised: 8 October 2018 / Accepted: 16 October 2018 / Published: 18 October 2018
(This article belongs to the Special Issue Numerical Methods for Partial Differential Equations)
It is well known that major error occur in the time integration instead of the spatial approximation. In this work, anisotropic kernels are used for temporal as well as spatial approximation to construct a numerical scheme for solving nonlinear Burgers’ equations. The time-dependent PDEs are collocated in both space and time first, contrary to spatial discretization, and time stepping procedures for time integration are then applied. Physically one cannot in general expect that the spatial and temporal features of the solution behaves on the same order. Hence, one should have to incorporate anisotropic kernels. The nonlinear Burgers’ equations are converted by nonlinear transformation to linear equations. The spatial discretizations are carried out to construct differentiation matrices. Comparisons with most available numerical methods are made to solve the Burgers’ equations. View Full-Text
Keywords: space–time numerical scheme; meshless method; radial kernels; Burgers’ equations space–time numerical scheme; meshless method; radial kernels; Burgers’ equations
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Uddin, M.; Ali, H. The Space–Time Kernel-Based Numerical Method for Burgers’ Equations. Mathematics 2018, 6, 212.

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