An Efficient New Scheme for Direct Simulation of Higher Order Third and Fourth Oscillatory Differential Equations

Abstract

In this research, we have examined the general block approach for solving higher-order oscillatory differential equations using the 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 problems were directly applied to the new method in order to overcome the setbacks of the reduction method. The results obtained were compared with those in the literature, and the new method takes away the burden of solving fourth-order oscillatory differential equations. Therefore, from the results, the new method has shown better accuracy and faster convergence graphically. One of the advantages of the new method is that it does not require much computational burden and is also self-starting. Convergence, Consistency, Direct simulation, Linear stability, Oscillatory differential equations