Highly accurate compact difference scheme for fourth order parabolic equation with Dirichlet and Neumann boundary conditions: application to good Boussinesq equation

DOI10.1016/j.amc.2020.125202zbMath1474.65279OpenAlexW3013385237MaRDI QIDQ2177904

Deepti Kaur, Ranjan Kumar Mohanty

Publication date: 7 May 2020

Published in: Applied Mathematics and Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.amc.2020.125202

zbMATH Keywords

singularitysolitoncompact difference schemeblock tridiagonal matrixfourth order parabolic equationgood Boussinesq equation

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Solitary waves for incompressible inviscid fluids (76B25) 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) Direct numerical methods for linear systems and matrix inversion (65F05) Soliton solutions (35C08) Numerical solution of discretized equations for initial value and initial-boundary value problems involving PDEs (65M22) Higher-order parabolic systems (35K41)

Related Items (5)

Finite difference schemes for the fourth‐order parabolic equations with different boundary value conditions ⋮ An adaptive approach for solving fourth-order partial differential equations: algorithm and applications to engineering models ⋮ The compact difference approach for the fourth‐order parabolic equations with the first Neumann boundary value conditions ⋮ High-order half-step compact numerical approximation for fourth-order parabolic PDEs ⋮ A new 2- level compact off-step implicit method in exponential form for the solution of fourth order nonlinear parabolic equations

Cites Work

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• Sextic B-spline collocation method for solving Euler-Bernoulli beam models
• New energy-preserving schemes using Hamiltonian boundary value and Fourier pseudospectral methods for the numerical solution of the ``good Boussinesq equation
• A meshless based numerical technique for traveling solitary wave solution of Boussinesq equation
• A note on solving the fourth-order parabolic equation by the sinc-Galerkin method
• A predictor-corrector scheme for the improved Boussinesq equation
• High accuracy implicit variable mesh methods for numerical study of special types of fourth order non-linear parabolic equations
• Euler-Bernoulli beams from a symmetry standpoint-characterization of equivalent equations
• A predictor-corrector scheme for the numerical solution of the Boussinesq equation
• 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
• A fourth order finite difference method for the good Boussinesq equation
• The solution of the Boussinesq equation using the method of lines
• Numerical investigation for the solitary waves interaction of the good Boussinesq equation.
• Efficient numerical algorithms for the solution of ``good Boussinesq equation in water wave propagation
• Unconditionally stable high accuracy compact difference schemes for multi-space dimensional vibration problems with simply supported boundary conditions
• A second order operator splitting numerical scheme for the ``good Boussinesq equation
• Local structure-preserving algorithms for the ``good Boussinesq equation
• A second order numerical scheme for the solution of the one-dimensional Boussinesq equation
• Two-level implicit high order method based on half-step discretization for 1D unsteady biharmonic problems of first kind
• Numerical Solutions of the Good Boussinesq Equation
• Soliton and antisoliton interactions in the ‘‘good’’ Boussinesq equation
• A fully Sinc-Galerkin method for Euler-Bernoulli beam models
• High accuracy two-level implicit compact difference scheme for 1D unsteady biharmonic problem of first kind: application to the generalized Kuramoto–Sivashinsky equation
• Linearized numerical schemes for the Boussinesq equation
• A <scp>Fourier</scp> pseudospectral method for the “good” <scp>Boussinesq</scp> equation with second‐order temporal accuracy

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