الفهرس 
Theory of Linear Approximation of FunctionsOnly 14 pages are availabe for public view
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Abstract
Summary
In recent years, numerical methods for partial differential equations
have enjoyed intense interest and development. This is due to the rapid
progress of high speed computers and also due to that many of most
significant problems for engineers and scientists can be formulated as
partial differential equations which can be solved in a satisfactory manner
by modern numerical methods. The method of finite differences is one of
most popular methods for the numerical solutions of partial differential
equations.
In this thesis, new finite difference schemes are constructed to
approximate the solutions of different problems in parabolic partial
differential equations in two-dimensional space. Also, new finite
difference schemes are constructed to approximate the solutions of
parabolic partial differential equations in the three-dimensional space.
These schemes are derived using the restrictive Pade and the restrictive
Taylor’s approximations which give high accurate results and have many
other advantage features. The stability conditions are studied fir the
suggested schemes. Comparisons of the numerical results obtained with
the classical methods are done .
Three papers have been extracted from this thesis which were
presented in national conferences held in Banha University and Military
Technical College as outlined below::
[1] Hassan N. A. Ismail and Ahmed R.A. Shafay ”Implicit Restrictive
Pade method for Almost Exact Solution for IBVPs for Two-
Dimensional Parabolic PDEs”, The 31’x’ International Conference for
Statistics, Computer Sciences and its Applications, Cairo, Vol. 2,
pp.37- 47 (2006).
[2] Hassan N. A. Ismail and Ahmed R.A. Shafay ”Explicit Restrictive
Taylor’s method For Almost Exact Solution for IBVPs for two-
Dimensional Parabolic PDEs”, fhe 31 th International Conference for
Statistics, Computer Sciences and its Applications, Cairo, Vol. 2,
pp.49- 59 (2006).
[3] Hassan N. A. Ismail and Ahmed R.A. Shafay ”Restrictive Taylor’s
Approximation for Higher Dimension IBV Problem for Parabolic
PDE”, The 3rd International Conference for Mathematics and
Engineering Physics ICMEP-3, M.T.C., Cairo, (2006), and sent for
possible publications in lnt. J. Computer Mathematics.