Discrete Petrov-Galerkin scheme for boundary value differential and integral problems: Theory and applications

DOI10.1016/j.mcm.2005.01.022zbMath1075.65105OpenAlexW1984131560MaRDI QIDQ2486773

Yanyan Li

Publication date: 17 August 2005

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

Full work available at URL: https://doi.org/10.1016/j.mcm.2005.01.022

zbMATH Keywords

convergencesingular perturbationnonlinear differential equationsnumerical experimentserror analysisnonlinear integrodifferential equationsdiscrete Petrov-Galerkin methodnonlinear side conditions

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Nonlinear boundary value problems for ordinary differential equations (34B15) Other nonlinear integral equations (45G10) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Singular perturbations for ordinary differential equations (34E15)

Related Items (2)

Schrödinger eigenbasis on a class of superconducting surfaces: ansatz, analysis, FEM approximations and computations ⋮ Discrete Galerkin method for Fredholm integro-differential equations with weakly singular kernels

Uses Software

• COLNEW
• COLSYS

Cites Work

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• A comparison of some global methods for solving two-point boundary value problems
• Optimal order spline methods for nonlinear differential and integro-differential equations
• A Deferred Correction Method for Nonlinear Two-Point Boundary Value Problems: Implementation and Numerical Evaluation
• A New Basis Implementation for a Mixed Order Boundary Value ODE Solver
• Collocation Software for Boundary-Value ODEs
• Collocation Methods for Integro-Differential Equations
• Approximative methods for nonlinear equations (two approaches to the convergence problem)
• Stability of discrete orthogonal projections for continuous splines
• Orthogonal collocation for a nonlinear integro-differential equation
• Collocation at Gaussian Points

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