Systems of nonlinear Volterra integro-differential equations

Authors:
Jalil Rashidinia;Ali Tahmasebi
Affiliations:
School of Mathematics, Iran University of Science and Technology, Tehran, Iran 16846-13114;School of Mathematics, Iran University of Science and Technology, Tehran, Iran 16846-13114
Venue:
Numerical Algorithms
Year:
2012

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Abstract

An efficient method based on operational Tau matrix is developed, to solve a type of system of nonlinear Volterra integro-differential equations (IDEs). The presented method is also modified for the problems with separable kernel. Error estimation of the new schemes are analyzed and discussed. The advantages of this approach and its modification is that, the solution can be expressed as a truncated Taylor series, and the error function at any stage can be estimated. Methods are applied on the four problems with separable kernel to show the applicability and efficiency of our schemes, specially for those problems at broad intervals.