Error analysis of a compact finite difference method for fourth-order nonlinear elliptic boundary value problems

DOI10.1016/j.apnum.2017.04.011zbMath1370.65063OpenAlexW2610673243MaRDI QIDQ2012617

Yuan-Ming Wang

Publication date: 1 August 2017

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2017.04.011

zbMATH Keywords

algorithmconvergenceerror estimateRichardson extrapolationcompact finite difference methodnumerical resultfourth-order nonlinear elliptic boundary value problem

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Nonlinear elliptic equations (35J60) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite difference methods for boundary value problems involving PDEs (65N06)

Related Items (7)

Numerical analysis for compact difference scheme of fractional viscoelastic beam vibration models ⋮ Superconvergent postprocessing of the \(C^1\)-conforming finite element method for fourth-order boundary value problems ⋮ A proper orthogonal decomposition-compact difference algorithm for plate vibration models ⋮ Compact difference scheme for <scp>two‐dimensional fourth‐order</scp> nonlinear hyperbolic equation ⋮ An efficient compact difference-proper orthogonal decomposition algorithm for fractional viscoelastic plate vibration model ⋮ Accuracy improvement of a predictor-corrector compact difference scheme for the system of two-dimensional coupled nonlinear wave equations ⋮ Compact difference scheme for two-dimensional fourth-order hyperbolic equation

Cites Work

• Nontrivial solutions and least energy nodal solutions for a class of fourth-order elliptic equations
• On fourth-order elliptic boundary value problems with nonmonotone nonlinear function
• On sign-changing solution for a fourth-order asymptotically linear elliptic problem
• Fourth-order compact finite difference method for fourth-order nonlinear elliptic boundary value problems
• Nonlinear fourth-order elliptic equations with nonlocal boundary conditions
• A note on a semilinear elliptic problem
• Full-order convergence of a mixed finite element method for fourth-order elliptic equations
• Some recent developments of Numerov's method
• High energy solutions of modified quasilinear fourth-order elliptic equations with sign-changing potential
• High-order compact solvers for the three-dimensional Poisson equation
• Monotone iterative technique for numerical solutions of fourth-order nonlinear elliptic boundary value problems
• Numerical methods for fourth-order nonlinear elliptic boundary value problems
• Maximum norm error bounds of ADI and compact ADI methods for solving parabolic equations
• Existence and uniqueness theorems for the bending of an elastic beam equation
• Analysis of Mixed Methods Using Mesh Dependent Norms
• Nontrivial solutions for some fourth order semilinear elliptic problems
• Multiplicity results for a fourth-order semilinear elliptic problem
• Block Monotone Iterations for Numerical Solutions of Fourth-Order Nonlinear Elliptic Boundary Value Problems
• On fourth-order elliptic boundary value problems
• Large-Amplitude Periodic Oscillations in Suspension Bridges: Some New Connections with Nonlinear Analysis
• Convergence of Fourth Order Compact Difference Schemes for Three‐Dimensional Convection‐Diffusion Equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Error analysis of a compact finite difference method for fourth-order nonlinear elliptic boundary value problems