Hybrid Numerical Method with Block Extension for Direct Solution of Third Order Ordinary Differential Equations  

作　　者：M. K. Duromola A. L. Momoh 

机构地区：[1]Department of Mathematical Sciences, Federal University of Technology, Akure, Ondo State, Nigeria

出　　处：《American Journal of Computational Mathematics》2019年第2期68-80,共13页美国计算数学期刊（英文）

摘　　要：This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the basis function for the solution of the IVP. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with five test problems including the Genesio equation to confirm its accuracy and usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the results with some existing methods shows the superiority of the accuracy of the method.This paper focuses on the development of a hybrid method with block extension for direct solution of initial value problems (IVPs) of general third-order ordinary differential equations. Power series was used as the basis function for the solution of the IVP. An approximate solution from the basis function was interpolated at some selected off-grid points while the third derivative of the approximate solution was collocated at all grid and off-grid points to generate a system of linear equations for the determination of the unknown parameters. The derived method was tested for consistency, zero stability, convergence and absolute stability. The method was implemented with five test problems including the Genesio equation to confirm its accuracy and usability. The rate of convergence (ROC) reveals that the method is consistent with the theoretical order of the proposed method. Comparison of the results with some existing methods shows the superiority of the accuracy of the method.

关 键 词：HYBRID Modified Block Grid POINTS Interpolation and COLLOCATION 

分 类 号：O1[理学—数学]