One-step methods for the numerical solution of linear differential equations based upon Lobatto quadrature formulae

The necessity of accurate numerical approximations to the solutions of differential equations governing physical systems has always been an important problem with scientists and engineers. Hammer and Hollingsworth [11] have used Gaussian quadrature for solving the linear second order differential equations. This method has been further developed by Morrison and Stoller [3], Korganoff [1], Kuntzman [9], Henrici [12] and Day [7, 8]. Quadrature methods based upon Lobatto quadrature formulae have recently been considered by Day [6, 8] and Jain and Sharma [10] and seem to give better results.