Numerical Simulation of One Step Block Method for Treatment of Second Order Forced Motions in Mass-Spring Systems
J. Sabo *
Department of Mathematics, Adamawa University, Mubi, Adamawa State, Nigeria.
T. Y. Kyagya
Department of Mathematics and Statistic, Federal University, Wukari, Taraba State, Nigeria.
W. J. Vashawa
Department of Medical Laboratory Technology, College of Health Technology, Michika, Adamawa State, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This paper discuss the numerical simulation of one step block method for treatment of second order forced motions in mass-spring systems of initial value problems. The one step block method has been developed with the introduction of off-mesh point at both grid and off- grid points using interpolation and collocation procedure to increase computational burden which may jeopardize the accuracy of the method in terms of error. The basic properties of the one step block method was established and numerical analysis shown that the one step block method was found to be consistent, convergent and zero-stable. The one step block method was simulated on three highly stiff mathematical problems to validate the accuracy of the block method without reduction, and obviously the results shown are more accurate over the existing method in literature.
Keywords: Block method, forced motions, initial value problems, mass-spring systems, numerical simulation, one step and treatment