HIGHER ORDER GAUSS-LEGENDRE QUADRATURE RUNGE-KUTTA TYPE METHOD FOR SOLVING STIFF AND OSCILLATORY PROBLEMS
DOI:
https://doi.org/10.33003/fjs-2026-1004-4861Keywords:
Implicit, More efficient, A-stable, Collocation methods, Perturbed Gaussian points, Order and Error constantAbstract
In this Paper a four (4) stage super convergent implicit Runge-Kutta type methods of order eight (8) have been constructed. [h1] [m2] [m3] This is an improvement of existing lower order four and six Gauss Legendre method for solving Ordinary Differential Equations (ODEs). Legendre polynomials of fourth degree basic function was used to generate the special Gaussian points for the construction of an implicit four points Gauss Legendre Runge-Kutta type methods. Collocation and matrix inversion approach is used to obtain continuous formulas for the method. The continuous formula is evaluated at the special Gaussian points of fourth-degree Legendre polynomials to yield a block discrete scheme which is converted to Runge-Kutta evaluation functions for the integration of Ordinary Differential Equations of ODEs, especially highly stiff and oscillatory problems of first order ODEs which are found in science and engineering models. Experimental problems used, show that the developed methods is A-stable, consistent, more efficient with less error estimate than the lower stage Gauss Legendre Runge-Kutta methods of order 4 and six respectively.
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Copyright (c) 2026 Zainab Adamu, Yakubu Muntaka Lawal, Aliyu Jaafar Bello
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