Solving fourth order differential equations using particular solutions of Helmholtz-type equations

DOI10.1016/j.aml.2018.06.012zbMath1416.65470OpenAlexW2810338215WikidataQ129610055 ScholiaQ129610055MaRDI QIDQ1726456

Wanru Chang, Wen Li, Ching-Shyang Chen

Publication date: 20 February 2019

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

Full work available at URL: https://doi.org/10.1016/j.aml.2018.06.012

zbMATH Keywords

Helmholtz equationparticular solutionsmethod of particular solutionspolynomial basis functions

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for second-order elliptic equations (35J25) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Higher-order elliptic equations (35J30) Preconditioners for iterative methods (65F08)

Related Items (8)

The local meshless method based on Pascal polynomial basis functions for solving fourth-order PDEs ⋮ A Comparative Study on Polynomial Expansion Method and Polynomial Method of Particular Solutions ⋮ A novel space-time meshless method for nonhomogeneous convection-diffusion equations with variable coefficients ⋮ Solving Fourth-Order PDEs using the LMAPS ⋮ The LMAPS for solving fourth-order PDEs with polynomial basis functions ⋮ An efficient MAPS for solving fourth order partial differential equations using trigonometric functions ⋮ An efficient method of approximate particular solutions using polynomial basis functions ⋮ Boundary function method for boundary identification in two-dimensional steady-state nonlinear heat conduction problems

Cites Work

• A new preconditioner for indefinite and asymmetric matrices
• The closed-form particular solutions for Laplace and biharmonic operators using a Gaussian function
• Chebyshev-type methods and preconditioning techniques
• Polynomial particular solutions for solving elliptic partial differential equations
• Method of particular solutions using polynomial basis functions for the simulation of plate bending vibration problems
• The method of approximate particular solutions for solving certain partial differential equations
• The Particular Solutions of Chebyshev Polynomials for Reissner Plates under Arbitrary Loadings
• A PRECONDITIONED METHOD FOR THE SOLUTION OF THE ROBBINS PROBLEM FOR THE HELMHOLTZ EQUATION
• A Modified Trefftz Method for Two-Dimensional Laplace Equation Considering the Domain's Characteristic Length
• Polynomial particular solutions for certain partial differential operators
• A Revisit on the Derivation of the Particular Solution for the Differential Operator ∆² ± λ²

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