Legendre cardinal functions and their applications in solving nonlinear stochastic differential equations

Document Type : Research Paper


Department of Mathematics, Faculty of Mathematics and Informatics, University of Bordj-Bou-Arreridj, Algeria


This paper presents a new numerical technique for solving stochastic Ito integral equations. A new operational matrix for integration of cardinal Legendre polynomials are introduced. By using this nexw operational matrix of integration and the so called collocation method, stochastic nonlinear integral equations are reduced to systems of algebraic equations with unknown coefficients. Only small dimension of Legendre operational matrix is needed to obtain a satisfactory results.
Some error estimations are provided and illustrative examples are also included to demonstrate the efficiency of the new technisue.


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Volume 13, Issue 2
July 2022
Pages 1757-1769
  • Receive Date: 13 July 2021
  • Revise Date: 18 October 2021
  • Accept Date: 16 December 2021