Eighth order Predictor-Corrector Method to Solve Quadratic Riccati Differential Equations

  • Wase Kassahun Jimma University
  • Alemayehu Shiferaw Jimma University
  • Solomon Gebregiorgis Jimma University
Keywords: Predictor-corrector method; Riccati differential equations; Stability analysis.

Abstract

In this paper, the eighth-order predictor-corrector method is presented for solving quadratic Riccati differential equations. First, the interval is discretized and then the method is formulated by using Newton’s backward difference interpolation formula. The stability and convergence of the method have been investigated. To validate the applicability of the proposed method, two model examples with exact solutions have been considered and numerically solved. Maximum absolute errors are presented in tables and figures for different values of mesh size h and the present method gives better results than some existing numerical methods reported in the literature.  

Author Biographies

Wase Kassahun, Jimma University

Department of Mathematics, Faculty of Natural Sciences, Jimma University, Jimma, Ethiopia

Alemayehu Shiferaw, Jimma University

Department of Mathematics, Faculty of Natural Sciences, Jimma University, Jimma, Ethiopia

Solomon Gebregiorgis, Jimma University

Department of Mathematics, Faculty of Natural Sciences, Jimma University, Jimma, Ethiopia

Published
2022-04-11
Section
Articles

Journal Identifiers


eISSN: 2220-184X
print ISSN: 2073-073X