Abstract: This paper discusses a novel method of exact discretization obtaining an equivalent difference equation whose solution is equal to the solution of a differential equation at discrete ...

Abstract: Differential equations are frequently used to analyze and design analog circuits and numerically solved from computation of difference equations. The equivalent difference equations are ...

An intermediate level course in the analytical and numerical study of ordinary differential equations, with an emphasis on their applications to the real world. Exact solution methods for ordinary ...

ABSTRACT: In this article, a new application to find the exact solutions of nonlinear partial time-space fractional differential Equation has been discussed. Firstly, the fractional complex ...

ABSTRACT: In previous papers, we proposed the important Z transformations and obtained general solutions to a large number of linear and quasi-linear partial differential equations for the first time.

$-2xy \sin( x^2) \d{x} + \cos(x^2) \d{y} = 0$ The ODE is already in the standard form so \begin{align} P &= -2xy \sin(x^2) \\ Q &= \cos(x^2) \\ \end{align} Check to ...