Numerical solution of Volterra integro-differential equations by superimplicit multistep collocation methods

DOI10.1007/s11075-014-9870-8zbMath1312.65220OpenAlexW2005315559MaRDI QIDQ2340359

Gholamreza Hojjati, Somayyeh Fazeli

Publication date: 16 April 2015

Published in: Numerical Algorithms (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11075-014-9870-8

zbMATH Keywords

convergencelinear stabilityVolterra integro-differential equationsnumerical experimentstiff problemmultistep collocation methods

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Other nonlinear integral equations (45G10) Volterra integral equations (45D05)

Related Items (13)

Taylor collocation method for a system of nonlinear Volterra delay integro-differential equations with application to COVID-19 epidemic ⋮ A class of two-step collocation methods for Volterra integro-differential equations ⋮ The Barycentric Rational Difference-Quadrature Scheme for Systems of Volterra Integro-differential Equations ⋮ Multistep collocation method for Fredholm integral equations of the second kind ⋮ Numerical methods for solving nonlinear Volterra integro-differential equations based on Hermite–Birkhoff interpolation ⋮ Multistep Runge-Kutta methods for Volterra integro-differential equations ⋮ Efficient general linear methods for a class of Volterra integro-differential equations ⋮ Block collocation boundary value solutions of the first-kind Volterra integral equations ⋮ Multistep collocation approximations to solutions of first-kind Volterra integral equations ⋮ Iterative Continuous Collocation Method for Solving nonlinear Volterra Integro-differential Equations ⋮ Stability analysis of Runge-Kutta methods for Volterra integro-differential equations ⋮ Collocation methods for Volterra integral and integro-differential equations: a review ⋮ On the numerical stability of the general linear methods for Volterra integro-differential equations

Cites Work

• Some interpolation theorems for polynomials
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• Multistep collocation methods for Volterra integral equations
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• On the integration of stiff systems of O.D.E.s using extended backward differentiation formulae
• Stability of numerical methods for Volterra integro-differential equations
• Super implicit multistep collocation methods for nonlinear Volterra integral equations
• New second derivative multistep methods for stiff systems
• Regions of Stability in the Numerical Treatment of Volterra Integro-Differential Equations
• Second Derivative Extended Backward Differentiation Formulas for the Numerical Integration of Stiff Systems
• The Construction of Reducible Quadrature Rules for Volterra Integral and Integro-differential Equations
• Collocation Methods for Volterra Integral and Related Functional Differential Equations
• Linear Multistep Methods for Volterra Integro-Differential Equations
• A special stability problem for linear multistep methods
• On Hermite-Birkhoff interpolation
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