Polynomial spline collocation methods for the nonlinear Basset equation

DOI10.1016/0898-1221(89)90239-3zbMath0687.65130OpenAlexW2061647481MaRDI QIDQ1263270

Hermann Brunner, Tao Tang

Publication date: 1989

Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0898-1221(89)90239-3

zbMATH Keywords

convergence ratesnonuniform gridsspline approximationsturbulent fluidNumerical testsBasset equationgrading exponentweakly singular nonlinear Volterra integro-differential equation

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Numerical methods for integral equations (65R20) Transonic flows (76H05) Singular nonlinear integral equations (45G05)

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Cites Work

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• A nonlinear weakly singular Volterra integro-differential equation arising from a reaction-diffusion study in a small cell
• The further study of a certain nonlinear integro-differential equation
• Numerical methods for singular nonlinear integrodifferential equations
• Collocation methods for Volterra integrodifferential equations with singular kernels
• A practical guide to splines
• Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels
• Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations
• More Generalised Discrete Gronwall Inequalities
• Fractional Linear Multistep Methods for Abel-Volterra Integral Equations of the Second Kind
• The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
• Weakly Singular Discrete Gronwall Inequalities
• Polynomial Spline Collocation Methods for Volterra Integrodifferential Equations with Weakly Singular Kernels
• Product Integration for Weakly Singular Integral Equations
• A piecewise polynomial approximation to the solution of an integral equation with weakly singular kernel
• 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
• Product Integration Methods for the Nonlinear Basset Equation
• Almost-periodic behavior of solutions of a nonlinear Volterra system.