Analytic and numerical solutions of nonlinear diffusion equations via symmetry reductions

作者：Verma Anjali; Jiwari Ram^*; Koksal Mehmet Emir

来源：Advances in Difference Equations, 2014, 2014(1): 229.

DOI：10.1186/1687-1847-2014-229

• nonlinear diffusion equations
• Lie classical method
• symmetry reduction
• differential quadrature method
• errors

In this article, the authors study analytic and numerical solutions of nonlinear diffusion equations of Fisher%26apos;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.

• 出版日期2014-8-20