Prusov V.A., Doroshenko A.Y.
Numerical method to solve the Cauchy problem with prehistory

The paper analyzes the theoretical aspects of constructing a family of single-stage multi-step methods for solving the Cauchy problem with prehistory for ordinary differential equations. The authors consider general issues related to discretization, approximation, convergence, and stability. The problem of improving the accuracy of numerical solutions is analyzed in detail. The results presented in the paper are also applicable for the numerical solution of partial differential equations. © 2017, Springer Science+Business Media New York.

Keywords: approximation, convergence, discretization, ordinary differential equations, single-stage multi-step method, strong stability, Numerical methods, Ordinary differential equations, Partial differential equations, Runge Kutta methods, approximation, convergence, Discretizations, Multi step methods, Strong stability, Problem solving

Cite:
Prusov V.A., Doroshenko A.Y. (2017). Numerical method to solve the Cauchy problem with prehistory. Cybernetics and Systems Analysis, 53 (1), 42-67. doi: https://doi.org/10.1007/s10559-017-9905-y http://jnas.nbuv.gov.ua/article/UJRN-0000621673 [In Russian].