Implementation of the One-Step One-Hybrid Block Method on the Nonlinear Equation of a Circular Sector Oscillator

TLDR: In this article, a single-step implicit block method involving one hybrid point with the introduction of a third derivative is proposed to solve nonlinear differential equation of a circular sector oscillator.

Abstract: Solving nonlinear differential equation of a circular sector oscillator is of a scientific importance. Thus, to solve such equations, a single- step implicit block method involving one hybrid point with the introduction of a third derivative is proposed. To derive this method, the approximate basis solution is interpolated at {xn, xn + 3/5} while its second and third derivatives are collocated at all points {xn, xn + 3/5, xn + 1}on the integrated interval of approximation. Numerical results are presented in the form of table and graphs for the variation of different physical parameters. The study reveals that the proposed hybrid block method is zero stable, which proves that it is convergent beside a significant interval of absolute stability, thus making it suitable for solving stiff ODEs.