Analytic and numerical solutions of nonlinear diffusion equations via symmetry reductions
ADVANCES IN DIFFERENCE EQUATIONS, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2014
- Doi Number: 10.1186/1687-1847-2014-229
- Journal Name: ADVANCES IN DIFFERENCE EQUATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Open Archive Collection: AVESIS Open Access Collection
- Ondokuz Mayıs University Affiliated: No
Abstract
In this article, the authors study analytic and numerical solutions of nonlinear diffusion equations of Fisher's type with the help of classical Lie symmetry method. Lie symmetries are used to reduce the equations into ordinary differential equations (ODEs). Lie group classification with respect to time dependent coefficient and optimal system of one-dimensional sub-algebras is obtained. Then sub-algebras are used to construct symmetry reduction and analytic solutions. Finally, numerical solutions of nonlinear diffusion equations are obtained by using one of the differential quadrature methods.