An operational method for solutions of Riccati type differential equations with functional arguments

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YÜZBAŞI Ş.

JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE, vol.14, no.1, pp.661-669, 2020 (SCI-Expanded) identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 1
  • Publication Date: 2020
  • Doi Number: 10.1080/16583655.2020.1761661
  • Journal Name: JOURNAL OF TAIBAH UNIVERSITY FOR SCIENCE
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED)
  • Page Numbers: pp.661-669
  • Keywords: Riccati differential equations, functional differential equations, operational matrix method, error analysis, HOMOTOPY PERTURBATION METHOD, MATRIX
  • Open Archive Collection: AVESIS Open Access Collection
  • Akdeniz University Affiliated: Yes

Abstract

In this article, an operational matrix approach is presented to solve the Riccati type differential equations with functional arguments. These equations are encountered in Mathematical Physics. The method is based on the least-squares approximation and the operational matrices of integration and product. By obtaining the operation matrices for each term of the problem, the method converts the problem to a system of nonlinear algebraic equations. The roots of last system are used in determination of unknown function. Error analysis is made. Numerical applications are given to show efficiency of the method and also the comparisons are made with other methods from literature. In applications of the method, it is observed from the applications that the suggested method gives effective results.