Algorithm 689

Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind. This paper describes a FORTRAN code for calculating approximate solutions to systems of nonlinear Volterra integral equations of the second kind. The algorithm is based on polynomial spline collocation, with the possibility of combination with the corresponding iterated collocation. It exploits certain local superconvergence properties for the error estimation and the stepsize strategy.

This software is also peer reviewed by journal TOMS.

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References in zbMATH (referenced in 8 articles , 1 standard article )

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  1. Isaacson, Samuel A.; Kirby, Robert M.: Numerical solution of linear Volterra integral equations of the second kind with sharp gradients (2011)
  2. Del Prete, Ida: Efficient numerical methods for Volterra integral equations of Hammerstein type (2007)
  3. Hoppensteadt, F. C.; Jackiewicz, Z.; Zubik-Kowal, B.: Numerical solution of Volterra integral and integro-differential equations with rapidly vanishing convolution kernels (2007)
  4. Conte, Dajana; Del Prete, Ida: Fast collocation methods for Volterra integral equations of convolution type (2006)
  5. Baker, Christopher T. H.: A perspective on the numerical treatment of Volterra equations (2000)
  6. Brunner, H.; Makroglou, A.; Miller, R. K.: On mixed collocation methods for Volterra integral equations with periodic solution (1997)
  7. Crisci, M. R.; Russo, E.; Vecchio, A.: Discrete-time waveform relaxation Volterra-Runge-Kutta methods: Convergence analysis (1997)
  8. Blom, J. G.; Brunner, H.: Algorithm 689: Discretized collocation and iterated collocation for nonlinear Volterra integral equations of the second kind (1991)