On the Numerical Approximation of Higher Order Differential Equation
Donald J. Zirra
Department of Mathematics, Faculty of Science, Adamawa State University, Mubi-650001, Nigeria.
Yusuf Skwame
Department of Mathematics, Faculty of Science, Adamawa State University, Mubi-650001, Nigeria.
John Sabo
*
Department of Mathematics, Faculty of Science, Adamawa State University, Mubi-650001, Nigeria.
Joshua A. Kwanamu
Department of Mathematics, Faculty of Science, Adamawa State University, Mubi-650001, Nigeria.
Silas Daniel
Department of Mathematics, Faculty of Science, Adamawa State University, Mubi-650001, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
This research examines the general K - step block approach for solving higher order oscillatory differential equations using Linear Block Approach (LBA). The basic properties of the new method such as order, error constant, zero-stability, consistency, convergence, linear stability and region of absolute stability were also analyzed and satisfied. Some distinct fourth order oscillatory differential equation were directly applied on the new method in order to overcome the setbacks in reduction method, where the step size varies. The results obtained were compared with those in literature and the new method takes away the burden of solving fourth order oscillatory differential equations. The accuracy of the new method proved to be better as it outperformed those of existing methods. Therefore, from the results, the new method has shown better accuracy and faster convergence graphically. One of the advantage of the new method is that it does not require much computational burden and it is also self-starting.
Keywords: Accuracy, computational burden, higher order IVPs, linear block approach