An algorithm for the Burgers’ equation using barycentric collocation method with a high-order exponential Lie-group scheme

Seydaoğlu, Muaz

doi:10.1007/s40096-022-00496-8

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Lie Group Geometric Integrator1

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2023

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“…Recently, KdV equation is solved by Polat and Oruç [52] via combination of Lie group scheme and DBFs, and accurate results are obtained. Furthermore, exponential Lie group scheme is proposed for Burgers equation by Seydaoglu [53]. Now, let us consider the system of ODEs given below:…”

Section: Lie Group Geometric Integratormentioning

confidence: 99%

A composite method based on delta‐shaped basis functions and Lie group high‐order geometric integrator for solving Kawahara‐type equations

Oruç,

Polat

2023

Math Methods in App Sciences

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In this paper, we devise a novel method to solve Kawahara‐type equations numerically. In this novel method, for spatial discretization, we use delta‐shaped basis functions and generate differentiation matrices for spatial derivatives of the Kawahara‐type equations. For discretization of temporal variable, we utilize a high‐order geometric numerical integrator based on Lie group methods. For illustration of efficiency of the suggested method, we consider some test problems. We calculate errors and make some comparisons with other results that exist in literature. We also report changes in conservation laws during numerical simulations, and we indicate that the suggested method can preserve the conservation laws pretty good. Outcomes of numerical simulations indicate that the suggested method in this paper is reliable and effective for nonlinear partial differential equations (PDEs).

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Section: Lie Group Geometric Integratormentioning

confidence: 99%