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The approximation properties and the conditions of convergence of a computational scheme of the generalized method of Lie-algebraic discrete approximations for the solution of the Cauchy problem with a one-dimensional advection equation are proved. The reduction of the Cauchy problem with the advection equation to a system of linear algebraic equations ensures the factorial convergence in all variables...
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...
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.
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