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

Kindybaliuk A.

Journal of Applied Mathematics and Computational Mechanics

2014

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.