On the Oscillation Criteria and Computation of Third Order Oscillatory Differential Equations

Abstract

One of the sets of differential equations that find applications in real life is the oscillatory problems. In this paper, the oscillation criteria and computation of third order oscillatory differential equations are studied. The conditions for a third order differential equation to have oscillatory solutions on the interval \(I=[t_0,\infty)\) shall be analyzed. Further, a highly efficient and reliable one-step computational method (with three partitions) is formulated for the approximation of third order differential equations. The paper also analyzed the basic properties of the method so formulated. The results obtained on the application of the method on some sampled modeled third order oscillatory problems show that the method is computationally reliable and the method performed better than the ones with which we compared our results.