1. Construction and Analysis of Explicit Adaptive One-Step Methods for Solving Stiff Problems
- Author
-
L. M. Skvortsov
- Subjects
010102 general mathematics ,MathematicsofComputing_NUMERICALANALYSIS ,Stability (learning theory) ,Stiffness ,Construct (python library) ,Explicit method ,01 natural sciences ,010101 applied mathematics ,Computational Mathematics ,symbols.namesake ,Ordinary differential equation ,Jacobian matrix and determinant ,medicine ,symbols ,Applied mathematics ,0101 mathematics ,medicine.symptom ,Eigenvalues and eigenvectors ,Mathematics - 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.
- Published
- 2020
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