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Construction and analysis of explicit adaptive one-step methods for solving stiff problems. (English. Russian original) Zbl 1451.65084
Comput. Math. Math. Phys. 60, No. 7, 1078-1091 (2020); translation from Zh. Vychisl. Mat. Mat. Fiz. 60, No. 7, 1111-1125 (2020).
Summary: 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.
MSC:
65L04 Numerical methods for stiff equations
65L20 Stability and convergence of numerical methods for ordinary differential equations
65L06 Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations
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