NUMERICAL SIMULATION OF STOCHASTIC DIFFERENTIAL EQUATIONS USING IMPLICIT MILSTEIN METHOD

journal article
Published by Institute of Research and Community Services Diponegoro University (LPPM UNDIP) in Journal of Fundamental Mathematics and Applications (JFMA)

Vol. 3 (1), 72-83
https://doi.org/10.14710/jfma.v3i1.7416

Abstract

Stiff stochastic differential equations arise in many applications including in the area of biology. In this paper, we present numerical solution of stochastic differential equations representing the Malthus population model and SIS epidemic model, using the improved implicit Milstein method of order one proposed in [6]. The open source programming language SCILAB is used to perform the numerical simulations. Results show that the method is more accurate and stable compared to the implicit Euler method.

Keywords

NUMERICAL SIMULATIONS
STOCHASTIC DIFFERENTIAL EQUATIONS
MILSTEIN METHOD
IMPLICIT MILSTEIN