Discrete and Combinatorial Mathematics: An Applied Introduction
Discrete and Combinatorial Mathematics: An Applied Introduction
Multistep collocation methods for Volterra Integral Equations
Applied Numerical Mathematics
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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.