Numerical application of third derivative hybrid block methods on third order initial value problem of ordinary differential equations

Abstract

The numerical application of third derivative on third order initial value problem of ordinary differential equations is consider in this paper. The method is derived by collocating and interpolating the approximate solution in power series, while Taylor series is used to generate the independent solution at selected grid and off grid points. The basic analysis of the method were established and it was found to be consistent, zero-stable and convergent. The developed method is then applied to solve some third order initial value problems of ODEs, and the result computed shows that the derived method is more accurate than some existing methods considered in this paper. We further plotted the solution graph of each problems and it is obvious that the numerical solution convergence toward the exact solution.