الفهرس 
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Abstract
Stochastic differential equations occur in the study of several physical phenomena and engineering sciences.Equation dealt with here are of ito type,and the like,driven by a wiener process brownian motion .The theory of such equations has attracted many researcheres and still a vivid research subject.
The present work is concerned with the numerical analysis simulation and computational aspects of both ordinary and partial stochastic differential equations.The main aim is to help applied mathematicians using success fully stochastic differential equations as models.New numerical schemes are proposed here by a modification of some previous one using a verified suggested estimator.
The numerical representation of the wiener process as a prerequisite data for solving stochastic differential equations numerically is given by the implementation of a generation method on digital computers.These results are used in the implementation of the suggested schemes to solve some examples numerically.Various tests are applied to ensure the coorectness of the results.Algorithms are given for all the above methods.Algorithm and programs are given as well.