A spectral collocation method based on Haar wavelets for Poisson equations and biharmonic equations

DOI10.1016/j.mcm.2011.07.006zbMath1235.65160OpenAlexW1994255226MaRDI QIDQ410005

Zhi Shi, Yong-Yan Cao

Publication date: 15 April 2012

Published in: Mathematical and Computer Modelling (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.mcm.2011.07.006

zbMATH Keywords

biharmonic equationPoisson equationHaar wavelet

Mathematics Subject Classification ID

Nontrigonometric harmonic analysis involving wavelets and other special systems (42C40) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Numerical methods for wavelets (65T60)

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Cites Work

• Unnamed Item
• A Galerkin boundary node method for biharmonic problems
• A high-order compact difference scheme for 2D Laplace and Poisson equations in non-uniform grid systems
• A fourth-order Poisson solver
• Solving fractional integral equations by the Haar wavelet method
• A spectral collocation technique based on integrated Chebyshev polynomials for biharmonic problems in irregular domains
• Multigrid solution of high order discretisation for three-dimensional biharmonic equation with Dirichlet boundary conditions of second kind
• A general meshsize fourth-order compact difference discretization scheme for 3D Poisson equation
• A spectral collocation method based on integrated Chebyshev polynomials for two-dimensional biharmonic boundary-value problems
• Multigrid method and fourth-order compact difference discretization scheme with unequal meshsizes for 3D Poisson equation
• A fast solver for the orthogonal spline collocation solution of the biharmonic Dirichlet problem on rectangles
• \(B\)-spline approximation and fast wavelet transform for an efficient evaluation of particular solutions for Poisson's equation
• Solving biharmonic problems with scattered-point discretization using indirect radial-basis-function networks
• An effective high order interpolation scheme in BIEM for biharmonic boundary value problems
• Solving integral and differential equations by the aid of non-uniform Haar wavelets
• Iterative method for solving the Neumann boundary value problem for biharmonic type equation
• The Numerical Evaluation of Particular Solutions for Poisson's Equation
• Solving high-order partial differential equations with indirect radial basis function networks
• New indirect scalar boundary integral equation formulas for the biharmonic equation