A survey of recent advances in the numerical treatment of Volterra integral and integro-differential equations

DOI10.1016/0771-050X(82)90044-4zbMath0485.65087MaRDI QIDQ1164400

Hermann Brunner

Publication date: 1982

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

bibliographyBibliographyresearch surveyweakly singular kernelsfirst and second kind

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Research exposition (monographs, survey articles) pertaining to numerical analysis (65-02) Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) (45E10) Volterra integral equations (45D05)

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Uses Software

• Algorithm 627

Cites Work

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• Collocation methods for Volterra integrodifferential equations with singular kernels
• Volterra integral equations
• Backward differentiation type formulas for Volterra integral equations of the second kind
• Superconvergence of collocation methods for Volterra and Abel integral equations of the second kind
• Convergence of linear multistep methods for Volterra first kind equations with k(t,t)=0
• The repetition factor and numerical stability of Volterra integral equations
• An extrapolation method with step size control for nonlinear Volterra integral equations
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• Implicit Runge-Kutta methods for second kind Volterra integral equations
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• A Volterra integral equation of the first kind
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• Sull' analisi numerica delle equazioni integrali di Volterra
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• On the Convergence of an Algorithm Computing Minimum-Norm Solutions of Ill-Posed Problems
• A note on a paper by luxemburg concerning the laplace transform
• Convergence and Stability Analysis for Modified Runge—Kutta Methods in the Numerical Treatment of Second-Kind Volterra Integral Equations
• On the Numerical Stability of Reducible Quadrature Methods for Second Kind Volterra Integral Equations
• Convergence and stability results in Runge-Kutta type methods for Volterra integral equations of the second kind
• Convergence of a Block-by-Block Method for Nonlinear Volterra Integro-Differential Equations
• The Construction of Reducible Quadrature Rules for Volterra Integral and Integro-differential Equations
• Runge-Kutta Theory for Volterra Integral Equations of the Second Kind
• Linear multistep methods for the numerical solution of volterra functional differential equations^†
• Numerical Methods for Nonlinear Volterra Integro-Differential Equations
• High Order Methods for a Class of Volterra Integral Equations with Weakly Singular Kernels
• Asymptotic Expansions for Product Integration
• Solving Nonlinear Second Kind Volterra Equations by Modified Increment Methods
• Automatic Integration of Functional Differential Equations: An Approach
• Application of Spline Functions to Systems of Volterra Integral Equations of the First and Second Kinds
• Stability and Convergence of Multistep Methods for Linear Volterra Integral Equations of the First Kind
• Stable Procedures for the Inversion of Abel′s Equation
• $A$-stable methods of high order for Volterra integral equations
• Global Solution of the Generalized Abel Integral Equation by Implicit Interpolation
• Sources and Applications of Integral Equations
• Analytically Solving Integral Equations by Using Computer Algebra
• Corrigendum
• The solution of Volterra integral equations of the first kind using inverted differentiation formulae
• A third order, semi-explicit method in the numerical solution of first kind Volterra integral equations
• Discretization of Volterra Integral Equations of the First Kind
• Taylor Series Methods for the Solution of Volterra Integral and Integro-Differential Equations
• Piecewise Polynomial Collocation for Volterra-type Integral Equations of the Second Kind
• The Solution of Volterra Integral Equations of the Convolution Type Using Two-Point Rational Approximants
• The application of the least squates finite element method to Abel's integral equation
• Numerical Solutions of a Class of Abel Integral Equations
• Cyclic Multistep Methods for Solving Volterra Integro-Differential Equations
• On optimal high accuracy linear multistep methods for first kind volterra integral equations
• On Numerically Solving Nonlinear Volterra Integral Equations with Fewer Computations
• Addendum to “Analytically Solving Integral Equations by Using Computer Algebra”
• Stability analysis of certain Runge-Kutta procedures for Volterra integral equations
• The Analysis of a Variable Step, Variable Coefficient Linear Multistep Method for Solving a Singular Integro–Differential Equation Arising from the Diffusion of Discrete Particles in a Turbulent Fluid
• Stability Regions in the Numerical Treatment of Volterra Integral Equations
• On a Nonlinear Integral Equation for Population Growth Problems
• Stability of quadrature rule methods for first kind volterra integral equations
• The numerical solution of volterra intergral equations with singular kernels
• A Starting Method for Solving Nonlinear Volterra Integral Equations
• A Method for Solving Nonlinear Volterra Integral Equations of the Second Kind
• Linear Multistep Methods for Volterra Integro-Differential Equations
• Numerial Methods for Volterra Integral Equations with Singular Kernels
• Numerical methods for Volterra integral equations of the first kind
• The numerical solution of nonlinear Volterra integral equations
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• Inversion of Abel’s Integral Equation by Means of Orthogonal Polynomials
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• Product integration methods for Volterra integral equations of the first kind
• One-Step Methods for the Numerical Solution of Volterra Functional Differential Equations
• The Numerical Solution of an Abel Integral Equation by a Product Trapezoidal Method
• Temperature of a nonlinearly radiating semi-infinite solid
• Convergence of Step-by-step Methods for Non-linear Integro-Differential Equations
• Predictor-corrector methods for nonlinear Volterra integral equations of the second kind
• A numerical solution of integral equation of the first kind applied to slit correction in small-angle x-ray scattering
• High Order Methods for Volterra Integral Equations of the First Kind
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• Spline Approximation to the Solution of the Volterra Integral Equation of the Second Kind
• On the numerical solution of nonlinear Volterra integro-differential equations
• Numerical solution of the abel integral equation
• The numerical solution of non-singular linear integral equations
• Numerical solution of Volterra integral equations
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