The RK1GL2X3 Method for Initial Value Problems in Ordinary Differential Equations

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.

• J.S.C. Prentice

• RK1GL2X3
• RK1GL2
• RKrGLm
• Runge-Kutta
• Gauss-Legendre
• initial value problem
• local error
• global error.

[1] J.S.C. Prentice, "The RKGL method for the numerical solution of initialvalue
problems", Journal of Computational and Applied Mathematics,
213, 2 (2008) 477 − 487
[2] J.S.C. Prentice, "General error propagation in the RKrGLm method",
Journal of Computational and Applied Mathematics, 228, (2009) 344 −
354.
[3] D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific
Computing, 3rd ed., Pacific Grove: Brooks/Cole, 2002, pp492 − 498.
[4] T.E. Hull, W.H. Enright, B.M Fellen, and A.E. Sedgwick, "Comparing
numerical methods for ordinary differential equations", SIAM Journal of
Numerical Analysis, 9, 4 (1972) 603 − 637.