On Thought Analysis of Numerical Scheme for Simulation Using a Kernel Optimum Nearly-Analytical Discretization (KOND) Method

Abstract

A thought analysis on numerical schemes for simulation is presented to lead to a new method called ‘Kernel Optimum Nearly-analytical Discretization (KOND) method’ for the construction of numerical schemes. The KOND method is applied to the two types of the hyperbolic and the parabolic equations. Typical numerical results by the KOND method for the hyperbolic equation are shown to clarify high stability and less numerical diffusion of the KOND scheme compared with other conventional schemes. A method for the digital signal processing of the analog signal f(t) with very high frequency components is proposed by using two thought elements of the KOND method.