According to this technique

finite difference solution is found by composing and solving linear equation system.

Finite Difference Scheme: To develop the

finite difference scheme for equation (1), we choose a digit and the time step from 0 to [?

AVM is more efficient than

finite difference since AVM solves Maxwell's equations twice no matter how many shape parameters one may have.

In order to solve these unsteady, non-linear coupled equations (7) to (10) with the condition (11), an implicit

finite difference scheme of Crank-Nicolson type has been employed.

Here we do not discuss the midpoint upwind

finite difference scheme [10] or streamline diffusion based on linear elements [11], because we want to compare approaches leading to four- or five-point schemes.

Without stability of

finite difference approximation, it is difficult to observe convergence property on the standard double precision arithmetic environments of computers, but it is possible to do it on a multiple-precision environment (e.

s]) is calculated by staggered-grid

finite difference method; [k.

Tensor-based extensions of

finite difference (FD) operators to higher spatial dimensions from their standard 1-D formulas is a well-known technique [9, 29].

A consistent 25-point

finite difference scheme for solving the 2D Helmholtz equation with PML was developed in [24].

Finite difference method replaces the main differential equation with the system of algebraic equations that links shifts of observed points relative to neighbouring points.

KEYWORDS: Pentaerythritol, Polyfunctionalized, Runge-kutta method, Non standard

finite difference method.

Keywords: Fourthorder parabolic partial differential equations Adomian decomposition method Polynomial cubicspline technique

Finite difference approximations Continuous approximation.