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A projection method for solving Cauchy singular integro-differential equations

Authors
Journal
Applied Mathematics Letters
0893-9659
Publisher
Elsevier
Volume
25
Issue
6
Identifiers
DOI: 10.1016/j.aml.2011.11.012
Keywords
  • Cauchy Kernel
  • Projection Approximation
  • Integro-Differential Equations
  • Legendre Polynomials
Disciplines
  • Mathematics

Abstract

Abstract In this work we present a modified projection method based on Legendre polynomials, for solving integro-differential equations with Cauchy kernel, in L2([−1,1],C). The proposed numerical procedure leads to solve a system of linear equations. We prove the existence of a solution for the approximate equation, and we perform the error analysis. Numerical examples illustrate the theoretical results.

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