Main Article Content
A general one-step hybrid block method with equidistant of order 6 has been successfully developed for the direct solution of second order IVPs in this article. Numerical analysis shows that the developed method is consistent and zero-stable which implies its convergence. The analysis of the new method is examined on two highly and mildly stiff second-order initial value problems to illustrate the efficiency of the method. It is obvious that our method performs better than the existing method within which we compare our result with. Hence, the approach is an adequate one for solving special second order IVPs.
Omar Z, Sulaiman M. Parallel r-point implicit block method for solving higher order ordinary differential equations directly. J. ICT. 2004;3:53-66.
James A, Adesanya A, Joshua S. Continuous block method for the solution of second order initial value problems of ordinary differential equation. Int. J. Pure Appl. Math. 2013;83:405-416.
Kayode SJ, Adeyeye O. A 3-step hybrid method for direct solution of second order initial value problems. Aust. J. Basic Appl. Sci. 2011;5:2121-2126.
Adesanya AO, Anake TA, Udo MO. Improved continuous method for direct solution of general second order ordinary differential equations. J. Niger. Assoc. Math. Phys. 2008;13:59-62.
Adeniran O, Ogundare B. An efficient hybrid numerical scheme for solving general second order initial value problems (IVPs). International Journal of Applied Mathematical Research. 2015;4:411-419.
Olanegan OO, Awoyemi DO, Ogunware BG, Obarhua FO. Continuous double-hybrid point method for the solution of second order ordinary differential equations. International Journal of Advanced Scientific and Technical Research. 2015;5:549-562.
Abdelrahim RF, Omar Z. Direct solution of second order ordinary differential equation using a single-step hybrid block method of order five. Mathematical and Computational Applications. 2016;21:1-12.
Kuboye JO, Omar Z, Abolarin OE, Abdelrahim R. Generalized hybrid block nmethod for solving second order ordinary differential equations directly. Research and Reports on Mathematics. 2018;2: 1-7.
Waeleh N, Majid ZA, Ismail F. A new algoriths for solving higher order IVPs of ODEs. Applied Mathematical Sciences. 2011;5:2795-2805.
Lambert J. Computational methods in ordinary differential equations. John Wiley & Sons, USA; 1973.
Henrici P. Discrete variable methods in ODEs. Wiley, New York; 1962.
Shampine LF, Watts HA. Block implicit one-step methods. Mathematics of Computation. 1969;731-740.
Dahlquist G. Convergence and stability in the numerical integration of ordinary differential equations. Mathematica Scandinavica. 1956;33-53.
Gear CW. Hybrid methods for initial value problems in ordinary differential equations. SIAM Journal of Numerical Analysis. 1965;2:69-86.
Jator SN. Solving second order initial value problems by a hybrid multi-step method without predictors. Applied Mathematics and Computation. 2010;8:4036-4046.
Alkasassbeh M, Omar Z. Implicit one-step block hybrid third-derivative method for the direct solution of initial value problems of second-order ordinary differential equations. Hindawi Journal of Applied Mathematics. 2017;1-8.
Kuboye JO, Omar Z, Abolarin OE, Abdelrahim R. Generalized hybrid block method for solving second order ordinary differential equations directly. Res Rep Math. 2018;2:1-7.