Olabode, B.T. (2007) Some Linear Multistep Methods for Special General Third Order Initial Value Problems of Ordinary Differential Equations. PhD Thesis, Federal University of Technology, Akure. (Unpublished)

has been cited by the following article:

• TITLE: On One-Step Method of Euler-Maruyama Type for Solution of Stochastic Differential Equations Using Varying Stepsizes

  AUTHORS: Sunday Jacob Kayode, Akeem Adebayo Ganiyu, Adegoke Sule Ajiboye

  KEYWORDS: One-Step Method, Ito Integral, Stochastic State Model, Gaussian White Noise, Wiener Process, Wiener Increment

  JOURNAL NAME: Open Access Library Journal, Vol.3 No.1, January 29, 2016

  ABSTRACT: In this work, a one-step method of Euler-Maruyama (EMM) type has been developed for the solution of general first order stochastic differential equations (SDEs) using Ito integral equation as basis tool. The effect of varying stepsizes on the numerical solution is also examined for the SDEs. Two problems of first order SDEs are solved. Absolute errors for the problems are obtained from which the mean absolute errors (MAEs) are calculated. Comparison of variation in stepsizes is achieved using the MAEs. The results show that the MAEs decrease as the stepsize decreases. The strong orders of convergence and the residuals for the problem for the theoretical are respectively obtained using Least Square Fit. This work produces numerical values for the solution to the problems which differ from the existing methods of EMM type in which results are always obtained by simulation.