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We discuss the structure of the local error of exponential operator splitting methods. In particular, it is shown that the leading error term is a Lie element, i.e., a linear combination of higher-degree commutators of the given operators. This structural assertion can be used to formulate a simple algorithm for the automatic generation of a minimal set of(More)
The paper deals with the local Cauchy problem for nonlinear functional differential systems. We investigate a general class of difference methods for this problem. We construct interpolating operators on the Haar pyramid and we give an error estimate for approximate solutions. We adopt nonlinear estimates of the Perron type for given functions with respect(More)
Problems of reconstructing unknown characteristics of dynamical systems through measurements of a part of the phase coordinates are embedded into the theory of inverse problems of dynamics. This theory is intensively developed at the present time. One of approaches to solving similar problems based on methods of the theory of positional control [1] was(More)
We consider initial boundary value problems for first order impulsive partial differential-functional equations. We give sufficient conditions for the convergence of a general class of one step difference methods. We assume that given functions satisfy the non-linear estimates of the Perron type with respect to the functional argument. The proof of(More)
The paper deals with the Darboux problem for the equation Dxyz(x, y) = f(x, y, z(x,y)) where z(x,y) is a function defined by z(x,y)(t, s) = z(x + t, y + s), (t, s) ∈ [−a0, 0]× [−b0, 0]. We construct a general class of difference methods for this problem. We prove the existence and uniqueness of solutions to implicit functional difference equations by means(More)
We give a theorem on implicit difference functional inequalities generated by mixed problems for nonlinear systems of first-order partial differential functional equations. We apply this result in the investigations of the stability of difference methods. Classical solutions of mixed problems are approximated in the paper by solutions of suitable implicit(More)
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