Variable Step Hybrid Block Method for the Approximation of Kepler Problem

In this article, a variable step size strategy is adopted in formulating new hybrid block method (VSHBM) for the solution of Kepler problem, which known to be rigid and stiff differential equation. To derive VSHBM, ratio r left same, halved, or doubled order optimize total number steps, minimize formulae stored code, ensure that zero-stable. The formulated by integrating Lagrange polynomial with limits integration selected at special points. article further analyzed stability, order, consistency, convergence properties VSHBM. stability regions VSHBM different values ratios were also plotted plots showed fit solving problem. results generated then compared some existing methods, including MATLAB inbuilt solver (ode 15 s), respect failure function calls, maximum error, computation time.