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The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations

Authors: J.S.C. Prentice


The RK1GL2X3 method is a numerical method for solving initial value problems in ordinary differential equations, and is based on the RK1GL2 method which, in turn, is a particular case of the general RKrGLm method. The RK1GL2X3 method is a fourth-order method, even though its underlying Runge-Kutta method RK1 is the first-order Euler method, and hence, RK1GL2X3 is considerably more efficient than RK1. This enhancement is achieved through an implementation involving triple-nested two-point Gauss- Legendre quadrature.

Keywords: initial value problem, Gauss-Legendre, Runge-Kutta, RKrGLm, local error, RK1GL2X3, RK1GL2, global error

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