Finite Difference Approximation Requiring Function Values on Non-Grid Points(Theory,<Special Topics>Activity Group "Scientific Computation and Numerical Analysis")

Abstract

We here investigate finite difference approximation requiring function values on non-grid points, while function values on grid points are employed in the conventional finite difference method. Such a finite difference approximation appears, for example, in deriving a finite difference scheme based on the method of characteristics for material derivative terms in flow problems. Introducing an interpolation operator to obtain the values on non-grid points, we evaluate the truncation error.