Abstract: We describe the RKrGLmXn
method for the numerical solution of initial-value problems. This method is
based on multiple nesting of the RKrGLm
method which, in turn, is based on an explicit Runge-Kutta method of order
r, and m-point Gauss-Legendre
quadrature. The order of RKrGLmXn
is where The maximal order of RKrGLmXn is 2m,
which can be significantly better than the underlying Runge-Kutta method.
Efficiency curves for RK2GL2X2, RK1GL2X3 and RK4GL3X2, as applied to a test
problem, are presented.
Keywords and phrases: RKrGLm, RKrGLmXn, Runge-Kutta, Gauss-Legendre, initial-value problem, order, local error, global error.
