A new solution method for stochastic differential equations via collocation approach

Abstract

The objective of this paper is to propose a novel solution method for Itô stochastic differential equations (SDEs). It is discussed that how the SDEs could numerically be solved as matrix problems. To improve the accuracy of this technique in contrast to the existing solvers, some non-uniform grids of points for discretizations along the time direction are applied. Finally, the high accuracy of approximated solutions in this way are illustrated by several experiments.

Keywords:

• stochastic differential equations
• collocation method
• Lamperti transform
• orthogonal polynomials

2010 AMS Subject Classifications:

• 65C30
• 60H35
• 65L60

Acknowledgments

The authors would like to record their sincerest thanks to three referees and the handling editor for several useful suggestions and criticisms, which resulted in an improved version of this work.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by a grant from Ferdowsi University of Mashhad [No. MA93318ARS].