Abstract
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.
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Translated from Kibernetika i Sistemnyi Analiz, No. 1, January–February, 2017, pp. 42–67.
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Prusov, V.A., Doroshenko, A.Y. Numerical Method to Solve the Cauchy Problem with Previous History. Cybern Syst Anal 53, 34–56 (2017). https://doi.org/10.1007/s10559-017-9905-y
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DOI: https://doi.org/10.1007/s10559-017-9905-y