الفهرس 
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Abstract
The random (stochastic) parabolic partial differential equation (RPPDE) is defined as partial differential equations involving random inputs (stochastic term). The initial, boundary conditions as well as the operator and inhomogeneous part of a partial differential equation are subjected to random uncertainties. For random variables or stochastic processes. Discuss stability and convergence, we have to follow different definitions than that of deterministic computations which agree with the facts of random variables and stochastic processes, mainly the existence of expectations or statistical moments of the random processes. Mean square (m.s) calculus was developed for such causes to enable the analysis of the problems associated with the existence of such processes with their statistical. The adaptation of the finite difference method to be used for solving such new problems needs the intensive use of the mean square calculus in the problem analysis. Various numerical methods and approximate schemes for RPDEs have also been developed. In this thesis the random finite difference method is used to obtain an approximate solution for random (stochastic) partial differential equations. The random (stochastic) finite difference techniques are based upon the approximations that permit replacing random (stochastic) partial differential equations by random (stochastic) finite difference equations. These finite difference approximations are algebraic in form, and the solutions are related to grid points. It is composed of three chapters. The 1st chapter is An introduction is given to review some subjects needed in the thesis. Chapter 2 Finite difference method used to approximate the solution of random parabolic partial differential equations using finite difference schems with three, five, and seven points. Also, study consistency, stability and convergence under mean square sense. There is also case study show the difference between the mean of the numerical relations with three, five, and seven points, and the mean of the exact relation which confirms the codition of convergense of the numerical relation to random parabolic partial differential equations under mean square sense. In chapter 3 Finite difference method used to approximate the solution of stochastic parabolic partial differential equations using finite difference schemes with three, five, and seven points, also study consistanc , stability and convergence under mean square sense .Finally, We disscused our results by numerical study.