Explicit Methods for Integrating Stiff Cauchy Problems

Abstract: An explicit method for solving stiff Cauchy problems is proposed. The method relies on explicit schemes and a step size selection algorithm based on the curvature of an integral curve. Closed-form formulas are derived for finding the curvature. For Runge–Kutta schemes with up to four stages, the corresponding sets of coefficients are given. The method is validated on a test problem with a given exact solution. It is shown that the method is as accurate and robust as implicit methods, but is substantially superior to them in efficiency. A numerical example involving chemical kinetics computations with 9 components and 50 reactions is given. © 2019, Pleiades Publishing, Ltd

Solution of stiff Cauchy problems with explicit schemes with geometrical-adaptive step selection

Abstract: We propose an explicit numerical method for solution of stiff Cauchy problems. The method implies explicit schemes and step selection procedure based on curvature of the integral curve. We propose explicit formulae for the curvature. For the Runge-Kutta schemes with up to 4 stages, the sets of the scheme coefficients are provided. Verification of the method is performed on a test problem with a known exact solution. We show that the method possesses the same accuracy and robustness as implicit methods and sufficiently excels them in efficiency.Note: Research direction:Mathematical problems and theory of numerical method