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A combined meshfree exponential Rosenbrock integrator for the third‐order dispersive partial differential equations
Author(s) -
Koçak Hüseyin
Publication year - 2021
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22726
Subject(s) - mathematics , exponential function , exponential integrator , partial differential equation , nonlinear system , euler's formula , integrator , korteweg–de vries equation , mathematical analysis , dissipation , differential equation , differential algebraic equation , ordinary differential equation , computer science , physics , computer network , bandwidth (computing) , quantum mechanics , thermodynamics
The aim of this study is to propose a combined numerical treatment for the dispersive partial differential equations involving dissipation, convection and reaction terms with nonlinearity, such as the KdV‐Burgers, KdV and dispersive‐Fisher equations. We use the combination of the exponential Rosenbrock–Euler time integrator and multiquadric‐radial basis function meshfree scheme in space as a qualitatively promising and computationally inexpensive method to efficiently exhibit behavior of such fruitful interactions resulting in antikink, two solitons and antikink‐breather waves. Obtained numerical solutions are compared with the existing results in the literature and discussed using illustrations in detail.