Affiliation:
1. Federal University Gashua
Abstract
Abstract
A research has been conducted at the Department of Mathematics, Faculty of Science, Federal University, Gashua, Yobe State to study the treatment of multistep collocation method for the direct solution of second order ordinary differential equations using a class of modified BDF-type with one super-future point. The research has proposed the construction of a new method of solving second-order initial valued problem of ordinary differential equation. A step-number, k = 3, a number of discrete members are obtained and used in block through multi-step collocation approach. The stability properties of the newly to be constructed methods are investigated using written computer codes and its convergence are established. The numerical efficiency of the method has been tested on some treated second-order initial valued problems, in order to ascertain its suitability. The solutions of the problems are compared with the corresponding exact solutions and the associated absolute errors are presented. Tables and graph have been adopted in the presentation of results. Conclusion and recommendation are made for further investigations.
Publisher
Research Square Platform LLC
Reference13 articles.
1. 1. J.C. Butcher, Numerical methods for ordinary differential equations in the 20th century, Journal of Computational and Applied Mathematics, 2000, 125, pp 1–29.
2. 2. Khadijah M. Abualnaja, A Block Procedure with Linear Multi-Step Methods Using Legendre Polynomials for Solving ODEs, Scientific Research Publishing Inc., 2015, 6, pp 717–723.
3. 3. Kaze Atsi and GM Kumleng, Block Extended Trapezoidal Rule of the Second Kind (Etr2) For the Direct Soltion of Second Order Initial Value Problems of Ordinary Differential Equations, IOSR Journal of Mathematics (IOSR-JM), 2021, 17(2), pp 10–14
4. 4. Kuboye J. O., Omar Z., Abolarin O. E. and Abdelrahim R., Generalized Hybrid Block Method for Solving Second Order Ordinary Differential Equations Directly, Research and Reports on Mathematics, 2018, 2(2), pp 1–7.
5. 5. Ra’ft Abdelrahim and Zurni Omar, Direct Solution of Second-Order Ordinary Differential Equation Using a Single-Step Hybrid Block Method of Order Five, Mathematical and Computational Applications, 2016, 21, 12; doi:10.3390/mca21020012.