A finite difference approach to find exact solution of differential equations
Abstract
This paper contains the background and samples of an approach to construct exact solutions of a wide range of differential equations (DEs). This approach is based on the finite difference equation which corresponds to the given DE. There are three cases considered: linear partial differential equation (PDE) with constant coefficients and at least one non-zero root of characteristic equation, linear PDE with constant coefficients and completely zero roots of the characteristic equation, and a case of nonlinear autonomous dynamical system of second order. Each of these cases is illustrated by an example.
- Publication:
-
International Journal of Modern Physics Conference Series
- Pub Date:
- April 2015
- DOI:
- 10.1142/S2010194515600800
- Bibcode:
- 2015IJMPS..3860080Z
- Keywords:
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- Finite difference equation;
- exact solutions;
- linear PDE;
- nonlinear autonomous dynamical systems