Defect correction and a posteriori error estimation of Petrov-Galerkin methods for nonlinear Volterra integro-differential equations.

DOI10.1023/A:1022333811602zbMath1058.65147MaRDI QIDQ1582530

Ming Rao, Tao Lin, Shuhua Zhang, Yan Ping Lin

Publication date: 15 October 2000

Published in: Applications of Mathematics (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/33058

zbMATH Keywords

asymptotic expansionsdefect correctionVolterra integro-differential equationsPetrov-Galerkin methodsa posteriori error estimators

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Error bounds for numerical methods for ordinary differential equations (65L70) Theoretical approximation of solutions to integral equations (45L05)

Related Items (3)

Superconvergence and postprocessing of the continuous Galerkin method for nonlinear Volterra integro-differential equations ⋮ Superconvergent postprocessing of the discontinuous Galerkin time stepping method for nonlinear Volterra integro-differential equations ⋮ Sparse representation of system of Fredholm integro-differential equations by using alpert multiwavelets

Cites Work

• A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations
• The method of lines for parabolic partial integro-differential equations
• An integrodifferential equation for rigid heat conductors with memory
• The numerical treatment of Volterra integro-differential equations with unbounded delay
• An immediate analysis for global superconvergence for integrodifferential equations
• An acceleration method for integral equations by using interpolation post-processing
• Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods
• Mixed interpolation collocation methods for first and second order Volterra integro-differential equations with periodic solution
• Superconvergence of numerical solutions to weakly singular Volterra integro-differential equations
• Runge-Kutta time discretizations of parabolic Volterra integro- differential equations
• Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels
• Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations
• A Priori $L^2 $ Error Estimates for Finite-Element Methods for Nonlinear Diffusion Equations with Memory
• Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
• A note on collocation methods for Volterra integro-differential equations with weakly singular kernels
• Evolutionary Integral Equations and Applications
• Stieltjes Derivatives and $\beta $-Polynomial Spline Collocation for Volterra Integrodifferential Equations with Singularities
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