Collocation methods for nonlinear Volterra integro-differential equations with infinite delay

In this paper we study the numerical solution of nonlinear Volterra integrodifferential equations with infinite delay by spline collocation and related Runge-Kutta type methods. The kernel function in these equations is of the form k(t, 8, y(t), y(s)), with a representative example given by Volterra's population equation, where we have k(t, a, y(t), y(8)) = a(t -s) . G(y(t), y(8))

[1]  J. B. McLeod,et al.  A nonlinear singularly perturbed Volterra integrodifferential equation occurring in polymer rheology , 1978, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[2]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[3]  Michael Renardy,et al.  A Nonlinear Volterra Integrodifferential Equation Describing the Stretching of Polymeric Liquids. , 1983 .

[4]  G. Webb.  Theory of Nonlinear Age-Dependent Population Dynamics , 1985 .

[5]  G. S. Jordan.  A nonlinear singularly perturbed Volterra integrodifferential equation of nonconvolution type , 1978, Proceedings of the Royal Society of Edinburgh: Section A Mathematics.

[6]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[7]  Vito Volterra.  The general equations of biological strife in the case of historical actions , 1939 .

[8]  Richard K Miller,et al.  Nonlinear Volterra Integral Equations , 1970 .

[9]  Takashi Kaminogo.  Continuous dependence of solutions for integrodifferential equations with infinite delay , 1988 .

[10]  Philip Rabinowitz,et al.  Methods of Numerical Integration , 1985 .

[11]  Jim M Cushing,et al.  Integrodifferential Equations and Delay Models in Population Dynamics , 1977 .

[12]  Hermann Brunner,et al.  Implicit Runge-Kutta Methods of Optimal Order for Volterra Integro-Differential Equations , 1984 .

[13]  Olavi Nevanlinna,et al.  Numerical Solution of a Singularly Perturbed Nonlinear Volterra Equation. , 1978 .

[14]  S. Levin.  Lectu re Notes in Biomathematics , 1983 .

[15]  H. Brunner,et al.  The numerical solution of Volterra equations , 1988 .

[16]  Shouchuan Hu,et al.  Nonlinear variation of parameters formula for integro-differential equations of Volterra type , 1988 .

[17]  R. K. Miller,et al.  Perturbation theory for Volterra integrodifferential systems , 1970 .

[18]  T. A. Burton,et al.  Stability and Periodic Solutions of Ordinary and Functional Differential Equations , 1986 .

[19]  James M. Ortega,et al.  Iterative solution of nonlinear equations in several variables , 2014, Computer science and applied mathematics.

[20]  R. K. Miller.  On Volterra’s Population Equation , 1966 .

[21]  V. Lakshmikantham,et al.  Equations with unbounded delay: a survey , 1980 .