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.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1071718Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1119
 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
 J.S.C. Prentice, "General error propagation in the RKrGLm method", Journal of Computational and Applied Mathematics, 228, (2009) 344 − 354.
 D. Kincaid and W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, 3rd ed., Pacific Grove: Brooks/Cole, 2002, pp492 − 498.
 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.