Generation of parallel colocation difference schemes using the integro-interpolation approach

Abstract

The issues of development of stable parallel difference schemes of a given order of accuracy, focused on the discretization of differential equations or their systems with concentrated and distributed parameters using an integro-interpolation approach to the generation of calculation coefficients, are considered. The proposed difference schemes improve the efficiency of parallel simulation and optimization of dynamic processes described by evolution equations with distributed parameters. Such equations are characterized by the absence of analytical solutions. The introduction of higher-order derivatives into difference schemes improves the accuracy of the obtained results and equalizes the approximation orders for all calculation points in the block.The proposed approach is universal for obtaining difference equations of various types. The computational formulas obtained on the basis of this approach for multipoint difference equations have less computational complexity and are oriented to implementation in computing systems with a parallel architecture.
 Keywords: integro-interpolation approach, difference schemes, colocation block methods, parallel computing