High accuracy combination method for solving the systems of nonlinear Volterra integral and integro-differential equations with weakly singular kernels of the second kind

DOI10.1155/2010/901587zbMath1192.65163OpenAlexW2046731378WikidataQ58653404 ScholiaQ58653404MaRDI QIDQ980664

Lu Pan, Xiaoming He, Tao Lü

Publication date: 29 June 2010

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

Full work available at URL: https://eudml.org/doc/231559

zbMATH Keywords

numerical examplesweakly singular kernelsa posteriori error estimationsecond kindhigh accuracy combination algorithmquadrature algorithmssystems of nonlinear Volterra integral and integro-differential equations

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Systems of nonlinear integral equations (45G15) Volterra integral equations (45D05) Singular nonlinear integral equations (45G05)

Related Items

A New Bernoulli Wavelet Method for Numerical Solutions of Nonlinear Weakly Singular Volterra Integro-Differential Equations, Sinc-Galerkin technique for the numerical solution of fractional Volterra-Fredholm integro-differential equations with weakly singular kernels, An operational matrix based scheme for numerical solutions of nonlinear weakly singular partial integro-differential equations, Two-dimensional wavelets operational method for solving Volterra weakly singular partial integro-differential equations

Cites Work

• Unnamed Item
• Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind
• Mechanical quadrature methods and their extrapolation for solving first kind Abel integral equations
• Higher accuracy methods for second-kind Volterra integral equations based on asymptotic expansions of iterated Galerkin methods
• A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equation of the second kind
• Spline collocation method for integro-differential equations with weakly singular kernels
• High accuracy combination algorithm and a posteriori error estimation for solving the first kind Abel integral equations
• The combination of approximate solutions for accelerating the convergence
• The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
• Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
• A Further Extension of the Euler-Maclaurin Summation Formula
• The Numerical Solution of Integral Equations of the Second Kind
• Numerical Quadrature and Asymptotic Expansions
• Fully Discrete Galerkin Method For Fredholm Integro-Differential Equations With Weakly Singular Kernels
• The discrete Petrov-Galerkin method for weakly singular integral equations