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

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.