NUMERICAL SOLUTIONS OF PROBLEMS FOR PARTIAL DIFFERENTIAL EQUATIONS AND APPLICATIONS

Abstract

Restriction of various types of approximation (Pade and Taylor approximations) of functions is a new technique established in 1995 by Ismail and Elbarbary [15] .This restriction type is constructed by supposing a parameter to be determined such that the error is equal to zero at certain point of the domain of the function . If this parameter reduces to zero , we get back the classical approximations .Many problems and applications have been treated by this method giving almost exact solution. Another category of methods for approximating the solution of PDEs is spectral collocation methods, which are described in many texts, for example, Canuto, et al.[4] . In these schemes, the solution is assumed to be a finite linear combination of some set of I;Jasis fuctions, and the function is .. discretized in the physical space at some chosen set of collocation points. The approximate solution is forced to satisfy the PDEonly at the collocation points.