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Zh. Vychisl. Mat. Mat. Fiz., 2020, Volume 60, Number 7, Pages 1111–1125 (Mi zvmmf11099)  

Construction and analysis of explicit adaptive one-step methods for solving stiff problems

L. M. Skvortsov

Bauman Moscow State Technical University, Moscow, 105005 Russia

Abstract: The paper considers the construction of adaptive methods based on the explicit Runge–Kutta stages. The coefficients of these methods are adjusted to the problem being solved, using component-wise estimates of the eigenvalues of the Jacobi matrix with the maximum absolute values. Such estimates can be easily obtained at the stages of the explicit method, which practically does not require additional calculations. The effect of computational errors and stiffness of the problem on the stability and accuracy of the numerical solution is studied. The analysis allows one to construct efficient explicit methods that are not inferior to implicit methods in solving many stiff problems. New nested pairs of adaptive methods are proposed, and the results of numerical experiments are presented.

Key words: ordinary differential equations, stiff Cauchy problem, explicit adaptive methods.

DOI: https://doi.org/10.31857/S0044466920070108


English version:
Computational Mathematics and Mathematical Physics, 2020, 60:7, 1078–1091

Bibliographic databases:

UDC: 519.622
Received: 29.12.2018
Revised: 26.12.2019
Accepted:10.03.2020

Citation: L. M. Skvortsov, “Construction and analysis of explicit adaptive one-step methods for solving stiff problems”, Zh. Vychisl. Mat. Mat. Fiz., 60:7 (2020), 1111–1125; Comput. Math. Math. Phys., 60:7 (2020), 1078–1091

Citation in format AMSBIB
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