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2 Journal of Applied Mathematics and Computational Mechanics

2 2014

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Generalized method of Lie-algebraic discrete approximations for solving Cauchy problems with evolution equation

100%

Kindybaliuk A.

tom Vol. 13, nr 2

51--62

We consider solving the Cauchy problem with an abstract linear evolution equation by means of the Generalized Method of Lie-algebraic discrete approximations. Discretization of the equation is performed by all variables in equation and leads to a factorial rate of convergence if Lagrange interpolation is used for building quasi representation of differential operator. The rank of a finite dimensional operator and approximation properties have been determined. Error estimations and the factorial rate of convergence have been proved.

Combined algorithm for finding conservation laws and implectic operators for the Boussinesq-Burgers nonlinear dynamical system and its finite dimensional reductions

63%

Kindybaliuk A. , Prytula M.

tom Vol. 13, nr 3

85--99

In the article the combined algorithm for finding conservation laws and implectic operators has been proposed. Using the Novikov-Bogoyavlensky method the finite dimensional reductions have been found. The structure of invariant submanifolds has been examined. Having analyzed phase portraits of Hamiltonian systems, partial periodical solutions have been found.