A functionally-fitted block hybrid Falkner method for Kepler equations and related problems.

Abstract

[EN]For the approximate solution of the Kepler equations and some related problems, a fourth-order convergent functionally-fitted block hybrid Falkner method which is based on the concepts of interpolation and collocation of the fitting function given as a linear combination of polynomials, hyperbolic and trigonometric functions is presented. The proposed method uses variable coefficients that are based on the product of the dominant frequency and the integration step length. This hybrid formula uses a block-wise implementation strategy to get over the difficulties of the predictor–corrector mode. In addition to being zero stable, the proposed method is applied to the Lambert–Watson linear stability test, which allows obtaining its stability region. Six numerical examples are provided to establish the performance of the proposed method.