Iterative reproducing kernel Hilbert spaces method for Riccati differential equations


Sakar M. G.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.309, pp.163-174, 2017 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 309
  • Publication Date: 2017
  • Doi Number: 10.1016/j.cam.2016.06.029
  • Journal Name: JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.163-174
  • Keywords: Iterative reproducing kernel Hilbert space method, Inner product, Riccati differential equation, Analytic approximation, Variable coefficient, TURNING-POINT PROBLEMS, NUMERICAL-SOLUTION
  • Van Yüzüncü Yıl University Affiliated: Yes

Abstract

This paper presents iterative reproducing kernel Hilbert spaces method (IRKHSM) to obtain the numerical solutions for Riccati differential equations with constant and variable coefficients. Representation of the exact solution is given in the W-2(2) [0, X] reproducing kernel space. Numerical solution of Riccati differential equations is acquired by interrupting the n-term of the exact solution. Also, the error of the numerical solution is monotone decreasing in terms of the norm of W-2(2)[0, X]. The outcomes from numerical examples show that the present iterative algorithm is very effective and convenient. (C) 2016 Elsevier B.V. All rights reserved.