NANASep 27, 2016

Shifted Chebyshev polynomials for Solving Three-Dimensional Volterra Integral Equations of the second kind

arXiv:1609.085397 citations
Originality Synthesis-oriented
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For researchers working on numerical solutions of integral equations, this is an incremental application of existing polynomial methods to a higher-dimensional problem.

The paper presents a method using shifted Chebyshev polynomials to solve three-dimensional Volterra integral equations of the second kind, transforming them into algebraic equations. Numerical results with error estimates are provided, but no concrete performance numbers are given.

In this paper, an efficient method is presented for solving three dimensional Volterra integral equations of the second kind with continuous kernel. Shifted Chebyshev polynomial is applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. Numerical results are calculated and the estimated error in each example is computed using Maple 17.

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