Restrictive taylor's approximation and parabolic partial differential equations

Abstract

In this paper we construct a restrictive type of Taylor's approximation of the function f(x) with parameter to be determined. It yields more accurate result, and it has the exact value at certain point. We shall develop a new approach for an explicit method to solve the parabolic partial differential equation. This approach will exhibit several advantages features: Highly accurate, fast, and the absolute error still very small whatever the exact solution is too large. The computational results, which are, presented show that computing time and memory space are saved with more accuracy. Stability conditions are obtained and utilized in numerical computations.