ABOUT THE NEW WAY FOR SOLVING SOME PHYSICAL PROBLEMS DESCRIBED BY ODE OF THE SECOND ORDER WITH THE SPECIAL STRUCTURE

Mathematical models for many theoretical and practical problems of natural sciences have been described by the ODEs. Such processes are common in the investigation of physical processes, which the scientists have begun to study from Newton (it is enough to remember Newton's laws). In recent times it often arises the necessity to construct mathematical models for some physical processes by using ODEs of the second order with the special structure (as the Schturm-Liouville, Scrhdinger and others problems). As is known there are wide classes of methods for solving the initial-value problem for the ODE of the second order with the special structures. One of the classical efficiency methods for solving these problems is the Strmer-Verlet method. Here, by developing this method have constructed the new class of hybrid methods with the constant coefficients.

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