Parallel multiple blocked methods of bickart type

Evgeniy A. Bashkow *a, Olga A. Dmitrieva**a, Nadiia H. Huskova***a,b, Magdalena Michalskac
a Donetsk National Technical University, Shybankova Square 2, 85300 Pokrovsk, Ukraine; bHigher Technical School of the University of Applied Sciences, Berlinstraße 109, 55411 Bingen, Germany; cLublin University of Technology, Nadbystrzycka 38 D, 20-618 Lublin, Poland

ABSTRACT
The article is devoted to the development and justification of parallel numerical simulation methods. Results can be obtained to calculate the number of points. To increase the order of approximation of the developed methods, the set of points of the reference block (s) is introduced into difference schemes. Generation of difference schemes for any reference and calculated points is considered. For some block sizes, generated differential calculation schemes are obtained, oriented to the number of available processes in a parallel implementation. The absolute stability of the constructed multi-step multipoint methods according to the initial conditions and the right side is proved.
Keywords: Cauchy problem, Bickart type methods, parallel modeling, difference schemes, block dimension, approximation order, stability