| Abstrakt: |
A unified explicit form for difference formulas to approximate fractional and classical derivatives is presented. The formula gives ginite difference approximations for any classical derivative with a desired order of accuracy at any nodal point in computational domain. It also gives Grüunwald type approximations for fractional derivatives with arbitrary order of approximation at any nodal point. Thus, this explicit form unifies approximations of both types of derivatives. Moreover, for classical derivatives, it also provides various finite difference formulas such as forward, backward, central, staggered, compact, non-compact, etc. efficient computations of the coefficients of the difference formulas are also presented leading to automating the solution process of differential equations with a given higher order accuracy. Some basic applications are presented to demonstrate the usefulness of this unified formulation. [ABSTRACT FROM AUTHOR] |
