Solution of the two dimensional second biharmonic equation with high‐order accuracy

DOI10.1108/03684920810884964zbMath1179.35110OpenAlexW2085944860MaRDI QIDQ3639393

Mehdi Dehghan, Akbar Mohebbi

Publication date: 30 October 2009

Published in: Kybernetes (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1108/03684920810884964

zbMATH Keywords

Dirichlet boundary conditions

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (4)

Finite pointset method for biharmonic equations ⋮ A new high accuracy finite difference discretization for the solution of 2D nonlinear biharmonic equations using coupled approach ⋮ On the numerical solution of high order multi-dimensional elliptic PDEs ⋮ A new high accuracy method for two-dimensional biharmonic equation with nonlinear third derivative terms: application to Navier–Stokes equations of motion

Cites Work

• Single cell discretizations of order two and four for biharmonic problems
• Multigrid solution of high order discretisation for three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind
• Direct solution of the biharmonic equation using noncoupled approach
• On an Alternating Direction Method for Solving the Plate Problem with Mixed Boundary Conditions
• GMRES: A Generalized Minimal Residual Algorithm for Solving Nonsymmetric Linear Systems
• CGS, A Fast Lanczos-Type Solver for Nonsymmetric Linear systems
• Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems
• Multigrid Solution of Automatically Generated High-Order Discretizations for the Biharmonic Equation
• Discretization Error Estimates for Certain Splitting Procedures for Solving First Biharmonic Boundary Value Problems
• A Transpose-Free Quasi-Minimal Residual Algorithm for Non-Hermitian Linear Systems
• The speed of convergence of one iterative process
• A relaxation method for solving elliptic difference equations
• High accuracy solution of three-dimensional biharmonic equations

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