Convergence analysis of spectral Tau method for fractional Riccati differential equations

Document Type: Research Paper

Authors

1 Muslim

2 muslim

Abstract

‎In this paper‎, ‎a spectral Tau method for solving fractional Riccati‎
‎differential equations is considered‎. ‎This technique describes‎
‎converting of a given fractional Riccati differential equation to a‎
‎system of nonlinear algebraic equations by using some simple‎
‎matrices‎. ‎We use fractional derivatives in the Caputo form‎.
‎Convergence analysis of the proposed method is given and rate of‎
‎convergence is established in the weighted $L^2-$norm‎. ‎Numerical‎
‎results are presented to confirm the high accuracy of the‎
‎method‎.

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Main Subjects



Volume 40, Issue 5
September and October 2014
Pages 1275-1290
  • Receive Date: 08 February 2013
  • Revise Date: 22 September 2013
  • Accept Date: 22 September 2013