Restrictive Chebyshev rational approximation and applications to heat-conduction problems

摘要

In this paper, we construct a restrictive type of Chebyshev rational approximation. It yields more accurate results and exact values at some selected points. We use this method to approximate the exponential function. We apply this approach to define a new implicit finite difference scheme to parabolic partial differential equations. This approach will exhibit several advantages features: highly accurate, fast, and the absolute error still very small whatever the exact solution is too large. Stability conditions are obtained and utilized in numerical computations. Finally, some numerical results to describe the performance of this approach are given.