Quasilinearization method for nonlinear differential equations with causal operators

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YAKAR A., Köksal M. E.

JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS, vol.9, no.3, pp.1356-1364, 2016 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 9 Issue: 3
  • Publication Date: 2016
  • Doi Number: 10.22436/jnsa.009.03.59
  • Journal Name: JOURNAL OF NONLINEAR SCIENCES AND APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.1356-1364
  • Keywords: Quasilinearization, differential equation, causal operator, nonlinearity, initial value problem, quadratic convergence, BOUNDARY-VALUE-PROBLEMS, TIME
  • Ondokuz Mayıs University Affiliated: Yes

Abstract

Employing quasilinearization technique coupled with the method of upper and lower solutions, we construct monotone sequences whose iterates are solutions to corresponding linear problems and show that the sequences converge uniformly and monotonically to the unique solution of the nonlinear problem with causal operator. Especially, instead of assuming convexity or concavity assumption on the nonlinear term that is demanded by the method of quasilinearization, we impose weaker conditions to be more useful in applications. The results obtained include several special cases and extend previous results. (C) 2016 All rights reserved.