Block Diagonally Implicit Runge-Kutta Method for Solving Ordinary Differential Equations - Rahim, Yong Faezah (2004)
Block diagonally implicit Runge-Kutta (BDIRK) method of second order is derived using Butcher analysis and equi-distribution of errors (EDE) approach to outperform standard Runge-Kutta formulae. BDIRK method produces simultaneously approximation to the solution of the initial value problem (IVP) at a block of two points and . Numerical results are given to illustrate the performance of the method and comparison is made to the standard Runge-Kutta method.