This article aims to derive, analyse, and implement an efficient one-step implicit hybrid method with block extension comprised of seven off-step points to directly solve Initial Value Problems (IVPs) of general four-...This article aims to derive, analyse, and implement an efficient one-step implicit hybrid method with block extension comprised of seven off-step points to directly solve Initial Value Problems (IVPs) of general four-order ordinary differential equations. For the resolution of the fourth-order IVPs, the exact was approximated by a polynomial termed basis function. The partial sum of the basis function and its fourth derivative were interpolated and collocated at some selected grid and off-grid points for the unknown parameters to be determined. The derived method, when tested, is found to be consistent, convergent, and zero-stable. The method’s accuracy and usability were experimented with using specific sample problems, and the findings revealed that it surpassed some cited methods in terms of accuracy.展开更多
文摘This article aims to derive, analyse, and implement an efficient one-step implicit hybrid method with block extension comprised of seven off-step points to directly solve Initial Value Problems (IVPs) of general four-order ordinary differential equations. For the resolution of the fourth-order IVPs, the exact was approximated by a polynomial termed basis function. The partial sum of the basis function and its fourth derivative were interpolated and collocated at some selected grid and off-grid points for the unknown parameters to be determined. The derived method, when tested, is found to be consistent, convergent, and zero-stable. The method’s accuracy and usability were experimented with using specific sample problems, and the findings revealed that it surpassed some cited methods in terms of accuracy.
