MODIFIED VERNER,RUNGE,KUTTA METHODS FOR THE NUMERICAL-SOLUTION OF INITIAL AND BOUNDARY-VALUE-PROBLEMS WITH ENGINEERING APPLICATIONS

Two new modified Runge-Kutta methods with minimal phase-lag are develo ped for the numerical solution of Ordinary Differential Equations with engineering applications. These methods are based on the well-known R unge-Kutta method of Verner RK6(5)9b (see J.H. Verner, some Runge-Kutt a formula pairs, SIAM J. Numer. Anal 28 (1991) 496-511) of order six. Numerical and theoretical results in some problems of the plate deflec tion theory show that this new approach is more efficient compared wit h the well-known classical sixth order Runge-Kutta Verner method. (C) 1998 Elsevier Science Inc. All rights reserved.