Numerov type variable mesh approximations for 1D unsteady quasi-linear biharmonic problem: application to Kuramoto-Sivashinsky equation

DOI10.1007/s11075-016-0154-3zbMath1358.65059OpenAlexW2419430033MaRDI QIDQ509637

Deepti Kaur, Ranjan Kumar Mohanty

Publication date: 17 February 2017

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-016-0154-3

zbMATH Keywords

stabilitynumerical resultsKuramoto-Sivashinsky equationextended Fisher-Kolmogorov equationsingular equationgeneralized fourth-order KdV equationunsteady quasi-linear biharmonic problemvariable mesh finite difference methods

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) KdV equations (Korteweg-de Vries equations) (35Q53) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12)

Related Items (8)

A class of quasi-variable mesh methods based on off-step discretization for the numerical solution of fourth-order quasi-linear parabolic partial differential equations ⋮ Robust Stackelberg controllability for the Kuramoto-Sivashinsky equation ⋮ A new 2-level implicit high accuracy compact exponential approximation for the numerical solution of nonlinear fourth order Kuramoto-Sivashinsky and Fisher-Kolmogorov equations ⋮ A new two-level implicit scheme of order two in time and four in space based on half-step spline in compression approximations for unsteady 1D quasi-linear biharmonic equations ⋮ High accuracy two-level implicit compact difference scheme for 1D unsteady biharmonic problem of first kind: application to the generalized Kuramoto–Sivashinsky equation ⋮ A class of two- and three-level implicit methods of order two in time and four in space based on half-step discretization for two-dimensional fourth order quasi-linear parabolic equations ⋮ Unconditionally stable high accuracy compact difference schemes for multi-space dimensional vibration problems with simply supported boundary conditions ⋮ High accuracy compact operator methods for two-dimensional fourth order nonlinear parabolic partial differential equations

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