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  5. Collocation block method with monitoring on step

Collocation block method with monitoring on step

O.A. Dmitrieva
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The article considers the questions with the creation of effective methods of parallel simulation of dynamic systems. Developed approaches suggest the possibility of automatic control integration step when the desired function (s) in certain areas characterized by different rates of change. Formation of calculation schemes is based on the multi-step collocation methods block with nonuniform arrangement of interpolation nodes in the support and settlement blocks, interconnected by any proportionality factor. For automatic generation of numerical schemes developed a software system based on the use of integro-interpolation method, which allows to generate coefficients for difference equations with arbitrary dimensions calculated and reference blocks, with the possibility of switching to the scheme stretching - compression step. If necessary, reduce the length of the step previously calculated values are used in the calculation scheme as intermediate, which can significantly reduce the number of computational operations. The obtained numerical solutions with different orders of approximation in the coinciding points calculated block formation provide error estimates for numerical integration.
Keywords: Cauchy problem, point collocation, integro-interpolation method, a support unit, settlement unit, integration step, the error