الفهرس 
Random Finite DifferenceOnly 14 pages are availabe for public view
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Abstract
In this thesis Random partial differential equation (RPDE) is defined as partial differential equations involving
random inputs. The initial and boundary conditions as well as the operator and inhomogeneous part of a partial
differential equation are subjected to random uncertainties. In this case the equation is called a random or
stochastic partial differential equation. For random variables or regular stochastic processes, the conventional
theories of differential equations still are in focus and the methods of solutions are valid after slight modifications.
In the case of irregular processes, the conventional calculus is no longer valid and new stochastic analysis is
needed. To 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.
The 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 properties, in the inputs of the differential equations see
[10-13]. 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 partial differential equations.
The random finite difference techniques are based upon the approximations that permit replacing random partial
differential equations by random finite difference equations. These finite difference approximations are algebraic
in form, and the solutions are related to grid points.