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

Content Provider	Springer Nature Link
Author	Mohanty, R. K. Kaur, Deepti
Copyright Year	2016
Abstract	We present two new two-level compact implicit variable mesh numerical methods of order two in time and two in space, and of order two in time and three in space for the solution of 1D unsteady quasi-linear biharmonic problem subject to suitable initial and boundary conditions. The simplicity of the proposed methods lies in their three-point discretization without requiring any fictitious points for incorporating the boundary conditions. The derived methods are shown to be unconditionally stable for a model linear problem for uniform mesh. We also discuss how our formulation is able to handle linear singular problem and ensure that the developed numerical methods retain their orders and accuracy everywhere in the solution region. The proposed difference methods successfully works for the highly nonlinear Kuramoto-Sivashinsky equation. Many physical problems are solved to demonstrate the accuracy and efficiency of the proposed methods. The numerical results reveal that the obtained solutions not only approximate the exact solutions very well but are also much better than those available in earlier research studies.
Ending Page	459
Page Count	33
Starting Page	427
File Format	PDF
ISSN	10171398
e-ISSN	15729265
Journal	Numerical Algorithms
Issue Number	2
Volume Number	74
Language	English
Publisher	Springer US
Publisher Date	2016-06-08
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Unsteady quasi-linear biharmonic problem Generalized fourth-order KdV equation Extended Fisher-Kolmogorov equation Singular equation Numeric Computing Theory of Computation Kuramoto-Sivashinsky equation Stability and convergence of numerical methods Solution of discretized equations Algorithms Algebra Numerical Analysis Variable mesh finite difference methods Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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