A novel collocation method based on residual error analysis for solving integro-differential equations using hybrid Dickson and Taylor polynomials

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Kürkçü Ö. K., Aslan E. n., Sezer M.

Sains Malaysiana, vol.46, no.2, pp.335-347, 2017 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 46 Issue: 2
  • Publication Date: 2017
  • Doi Number: 10.17576/jsm-2017-4602-19
  • Journal Name: Sains Malaysiana
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.335-347
  • Keywords: Collocation and matrix methods, Dickson and Taylor polynomials, Integro-differential equations, Nonlinear equations, Pseudocode
  • Open Archive Collection: AVESIS Open Access Collection
  • Manisa Celal Bayar University Affiliated: Yes

Abstract

In this study, a novel matrix method based on collocation points is proposed to solve some linear and nonlinear integrodifferential equations with variable coefficients under the mixed conditions. The solutions are obtained by means of Dickson and Taylor polynomials. The presented method transforms the equation and its conditions into matrix equations which comply with a system of linear algebraic equations with unknown Dickson coefficients, via collocation points in a finite interval. While solving the matrix equation, the Dickson coefficients and the polynomial approximation are obtained. Besides, the residual error analysis for our method is presented and illustrative examples are given to demonstrate the validity and applicability of the method.