Differential equations, difference equations and matrix theory

Nonstandard finite difference schemes for differential equations

In this paper, the reorganization of the denominator of the discrete derivative and nonlocal approximation of nonlinear terms are used in the design of nonstandard finite difference schemes (NSFDs). Numerical examples confirming then efficiency of schemes, for some differential equations are provided. In order to illustrate the accuracy of the new NSFDs, the numerical results are compared with ...

Qualitative Theory of Differential Equations, Difference Equations, and Dynamic Equations on Time Scales

1School of Informatics, Linyi University, Linyi, Shandong 276005, China 2Department of Mathematics and Statistics, Missouri S&T, Rolla, MO 65409-0020, USA 3Department of Mathematics, Faculty of Arts and Sciences, Niğde University, 51200 Niğde, Turkey 4Department of Mathematical Sciences, University of Agder, Postboks 422, 4604 Kristiansand, Norway 5School of Mathematics, Sun Yat-sen University,...

Linear difference and differential equations

Nonlinear difference-differential equations in prediction and learning theory.

1. Introduction.-This note introduces some nonlinear difference-differential equations which can be interpreted as a learning theory or, alternatively, as a prediction theory whose goal is to discuss the prediction of individual events, in a fixed order, and at prescribed times. The theory provides a mathematical description of the following kind of experiment. An experimenter g, confronted by ...

Finite difference method for solving partial integro-differential equations

In this paper, we have introduced a new method for solving a class of the partial integro-differential equation with the singular kernel by using the finite difference method. First, we employing an algorithm for solving the problem based on the Crank-Nicholson scheme with given conditions. Furthermore, we discrete the singular integral for solving of the problem. Also, the numerical results ob...