This book provides a clear summary of the work of the author on the construction of nonstandard finite difference schemes for the numerical integration of differential equations. The major thrust of ...

Abstract: We show that applying a generalization of the Cayley-Hamilton Theorem to a state-space representation of a single-output, multidimensional (mD), linear, shift-invariant, causal, autonomous ...

The present paper considers the stochastic difference equation Yn=AnYn-1+Bn with i.i.d. random pairs (An,Bn) and obtains conditions under which Yn converges in ...

This repository serves to solve, partial differential equation using finite difference's equation, the equation in discuss is given by, $$\frac{\partial T}{\partial t} = \alpha \frac{\partial^2 ...

IN his preface, the author states that this volume includes material for a course in finite differences as well as a treatment of a number of special topics. A selection of material was necessary in ...

In this paper, two fourth-order accurate compact difference schemes are presented for solving the Helmholtz equation in two space dimensions when the corresponding wave numbers are large. The main ...

Abstract: To filter out noise in transient electromagnetic (TEM) signals, a Time-Space Fractional-order Diffusion Model (TSFDM) based on intelligent optimization is proposed. Firstly, based on the ...