الفهرس 
Historical note and literature survey
Rothe’s method for partial differential equationsOnly 14 pages are availabe for public view
 |  | from | 38 |  |  |
| | | from | 38 | | |
Abstract
Spline Functions introduce a great importance in several science branches as in numerical analysis, ordinary, partial differential equations, integral equations and statistical analysis. Also, it has many applications in science, Engineering, Economics, Biology and Medicine etc. In this thesis, we study cubic exponential spline in calculating numerical solutions for two parameter singular perturbed parabolic partial differential equations. Also, we use septic exponential spline in calculating numerical solutions for fourth order parabolic partial differential equations. Exponential spline function is composed of two parts; the first part is an exponential function, while the second part is a polynomial function. This thesis contains four chapters, and is organized as follows: In chapter (I), contains survey of the previous studies related to this field. In chapter (II), we consider the approximate solution of one dimensional parabolic equation and higher order parabolic differential equations by using Rothe’s method. A new discretization scheme is introduced. The numerical results are compared with the exact solution.