الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
This thesis which deals with the numerical treatment of partial differential equations contains four chapters : The first chapter is considered as fundamentals. during the last ten years engineers and scientists in all fields have used partial differential equations to describe an increasingly large number of their problems. A knowledge of the methods for obtaining numerical results is very important, and numerical solution using high speed digital computers is the only recourse. Soon after runge discovered his method of solving ordinary differential equations, gauss extended the method to partial differential equations with given initial conditions. Some years later willers extended the improved runge -kutta method to the solution of partial differential equations. These methods are slow and laborious and have not come into general use. Thus we are going to search for some practical methods to be used conveniently.
Certain types of boundary-value problems can be solved by replacing the partial differential equation by the corresponding difference equation and then solving the later by s process of iteration. This method was devised and first used by richardson. It was later improved by liebmann and further improved more recently by stortley and weller. The process is slow but gives good results on boundary - value problems. A strong point in its favor is that the computation can be done by an automatic sequence controlled calculating machine. Typical partial differential equation of partical importance are illustrated.
In the second chapter, the straight method is developed for solving partial differential equations. by means of this method, the partial differential equations with boundary conditions are approximated to a system of boundary conditions ordinary differential equations. In general , we can obtain systems of different accuracy of ordinary differential equations.