Legendre expansion method for the solution of the second-and fourth-order elliptic equations

DOI10.1016/S0378-4754(01)00421-9zbMath1004.65120OpenAlexW2016018528MaRDI QIDQ1614034

Elsayed M. E. Elbarbary

Publication date: 3 September 2002

Published in: Mathematics and Computers in Simulation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0378-4754(01)00421-9

zbMATH Keywords

numerical resultsbiharmonic equationHelmholtz equationLegendre polynomialsspectral methods

Mathematics Subject Classification ID

Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Boundary value problems for higher-order elliptic equations (35J40) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Biharmonic, polyharmonic functions and equations, Poisson's equation in two dimensions (31A30)

Related Items (11)

Error analysis of the Chebyshev collocation method for linear second-order partial differential equations ⋮ A matrix method for solving high-order linear difference equations with mixed argument using hybrid Legendre and Taylor polynomials ⋮ Combining Legendre's polynomials and genetic algorithm in the solution of nonlinear initial-value problems ⋮ Error upper bounds for a computational method for nonlinear boundary and initial-value problems ⋮ Direct computation of operational matrices for polynomial bases ⋮ Solving high-order linear differential equations by a Legendre matrix method based on hybrid Legendre and Taylor polynomials ⋮ Bernstein series solution of linear second-order partial differential equations with mixed conditions ⋮ Comparison of Legendre polynomial approximation and variational iteration method for the solutions of general linear Fredholm integro-differential equations ⋮ Dirac's formalism combined with complex Fourier operational matrices to solve initial and boundary value problems ⋮ Legendre polynomial solutions of high-order linear Fredholm integro-differential equations ⋮ Legendre Collocation Method to Solve the Riccati Equations with Functional Arguments

Cites Work

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• A practical chebyshev collocation method for differential equations
• Chebyshev Polynomials in the Numerical Solution of Differential Equations
• Efficient Spectral-Galerkin Method I. Direct Solvers of Second- and Fourth-Order Equations Using Legendre Polynomials
• Efficient Spectral-Galerkin Method II. Direct Solvers of Second- and Fourth-Order Equations Using Chebyshev Polynomials

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