Direct computation of operational matrices for polynomial bases

DOI10.1155/2010/139198zbMath1198.65121OpenAlexW2168998793WikidataQ58652923 ScholiaQ58652923MaRDI QIDQ1958795

Marcio Lobo Netto, Osvaldo Guimarães, José Roberto Castilho Piqueira

Publication date: 30 September 2010

Published in: Mathematical Problems in Engineering (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/228348

zbMATH Keywords

boundary value problemsintegrationdifferentiationoperational matriceslinear operationpolynomial bases

Mathematics Subject Classification ID

Numerical solution of boundary value problems involving ordinary differential equations (65L10) Linear boundary value problems for ordinary differential equations (34B05)

Related Items (9)

Solving 2nd order BVPs in planar irregular domains ⋮ Tensor solutions in irregular domains: eigenvalue problems ⋮ Combining Legendre's polynomials and genetic algorithm in the solution of nonlinear initial-value problems ⋮ Novel approach to spectral methods for irregular domains ⋮ Error upper bounds for a computational method for nonlinear boundary and initial-value problems ⋮ Generalized operational matrices and error bounds for polynomial basis ⋮ Coadjoint formalism: nonorthogonal basis problems ⋮ Dirac's formalism combined with complex Fourier operational matrices to solve initial and boundary value problems ⋮ Structural analysis of matrix integration operators in polynomial bases

Cites Work

• Efficient spectral-Galerkin algorithms for direct solution of fourth-order differential equations using Jacobi polynomials
• Defeating the Runge phenomenon for equispaced polynomial interpolation via Tikhonov regularization
• Taylor polynomial solutions of linear differential equations.
• Legendre expansion method for the solution of the second-and fourth-order elliptic equations
• Numerical solution of differential equations by using Chebyshev wavelet operational matrix of integration
• The linear Legendre mother wavelets operational matrix of integration and its application
• Orthogonal polynomials of discrete variable and boundedness of Dirichlet kernel
• A computational method for solving optimal control of a system of parallel beams using Legendre wavelets
• Error Estimates in Sobolev Spaces for Moving Least Square Approximations
• The Legendre wavelets operational matrix of integration
• 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
• Polynomial solutions of certain differential equations
• Runge-Kutta type methods for orthogonal integration
• Unnamed Item

This page was built for publication: Direct computation of operational matrices for polynomial bases