Том 71
№ 11

All Issues

Dushka V. A.

Articles: 1
Article (Ukrainian)

Diffusive Lotka-Volterra System: Lie Symmetries and Exact and Numerical Solutions

Cherniga R. M., Dushka V. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2004. - 56, № 10. - pp. 1395-1404

We present a complete description of Lie symmetries for the nonlinear diffusive Lotka-Volterra system. The results are used for the construction of exact solutions of the Lotka-Volterra system, which, in turn, are used for solving the corresponding nonlinear boundary-value problems with zero Neumann conditions. The analytic results are compared with the results of computation based on the finite-element method. We conclude that the obtained exact solutions play an important role in solving Neumann boundary-value problems for the Lotka-Volterra system.