Numerical simulations of Kuramoto-Sivashinsky equation in reaction-diffusion via Galerkin method

DOI10.1007/s40096-021-00402-8zbMath1473.65191OpenAlexW3159546430MaRDI QIDQ2041190

Ozlem Ersoy Hepson

Publication date: 15 July 2021

Published in: Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40096-021-00402-8

zbMATH Keywords

Galerkin methodstability analysisKuramoto-Sivashinsky equationquartic trigonometric tension B-splines

Mathematics Subject Classification ID

Reaction-diffusion equations (35K57) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60)

Related Items (4)

Trigonometric B-spline based ε-uniform scheme for singularly perturbed problems with Robin boundary conditions ⋮ Study of \(4^{th}\) order Kuramoto-Sivashinsky equation by septic Hermite collocation method ⋮ A numerical scheme for the wave simulations of the Kuramoto-Sivashinsky model via quartic-trigonometric tension B-spline ⋮ Numerical simulations of reaction-diffusion systems in biological and chemical mechanisms with quartic-trigonometric B-splines

Cites Work

• Meshless method of lines for the numerical solution of generalized Kuramoto-Sivashinsky equation
• Quintic B-spline collocation method for numerical solution of the Kuramoto-Sivashinsky equation
• Numerical solutions of the generalized Kuramoto-Sivashinsky equation by Chebyshev spectral collocation methods
• The non-existence of a certain class of travelling wave solutions of the Kuramoto-Sivashinsky equation
• A quintic B-spline based differential quadrature method for numerical solution of Kuramoto-Sivashinsky equation
• Generalization of Gegenbauer wavelet collocation method to the generalized Kuramoto-Sivashinsky equation
• A numerical algorithm based on a new kind of tension B-spline function for solving Burgers-Huxley equation
• On the well-posedness of an anisotropically-reduced two-dimensional Kuramoto-Sivashinsky equation
• Local discontinuous Galerkin methods for the Kuramoto-Sivashinsky equations and the Ito-type coupled KdV equations
• Numerical solutions of the generalized kuramoto-sivashinsky equation using B-spline functions
• Extended tanh-function method and its applications to nonlinear equations
• The exponential cubic B-spline collocation method for the Kuramoto-Sivashinsky equation

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