Numerical solution of first order initial value problem using 4-stage sixth order Gauss-Kronrod-Radau 1 method - Teh, Yuan Ying; Yaacob, Nazeeruddin (2011)
In this paper, we consider a new implicit Runge-Kutta method which based on 4-point Gauss-Kronrod-Radau I quadrature formula, or in brief as GKRM(4,6)-I. The resulting implicit method is a 4-stage sixth order Gauss Kronrod-Radau I method.In addition, GKRM(4,6)-I has stage order 4. Numerical results compare the accuracy between GKRM(4,6)-I and the classical 3-stage sixth order Gauss-Legendre method in solving some test problems.Numerical results reveal that GKRM(4,6)-I is more accurate than the 3-stage sixth order Gauss-Legendre method because GKRM(4,6)-I has higher stage order.