Local Error Control in the RK5GL3 Method

The RK5GL3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on a combination of a fifth-order Runge-Kutta method and 3-point Gauss-Legendre quadrature. In this paper we describe an effective local error control algorithm for RK5GL3, which uses local extrapolation with an eighth-order Runge-Kutta method in tandem with RK5GL3, and a Hermite interpolating polynomial for solution estimation at the Gauss-Legendre quadrature nodes.

Authors:

• J.S.C. Prentice

Keywords:

• RK5GL3
• RKrGLm
• Runge-Kutta
• Gauss-Legendre
• Hermite interpolating polynomial
• initial value problem
• local error.

References:

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