Multistep Hermite collocation methods for solving Volterra Integral Equations

Multistep Hermite collocation methods for solving Volterra Integral Equations

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Article ID: iaor20123757
Volume: 60
Issue: 1
Start Page Number: 27
End Page Number: 50
Publication Date: May 2012
Journal: Numerical Algorithms
Authors: , ,
Keywords: differential equations
Abstract:

In this paper, we propose a new class of multistep collocation methods for solving nonlinear Volterra Integral Equations, based on Hermite interpolation. These methods furnish an approximation of the solution in each subinterval by using approximated values of the solution, as well as its first derivative, in the r previous steps and m collocation points. Convergence order of the new methods is determined and their linear stability is analyzed. Some numerical examples show efficiency of the methods.

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