%0 Journal Article %T \(4\)-step \(5\)-point hybrid block method for the direct solution of second order initial value problems %A Oluwaseun, Adeyeye %J Journal of Mathematics and Computer Science %D 2017 %V 17 %N 4 %@ ISSN 2008-949X %F Oluwaseun2017 %X Block methods for the numerical solution of ordinary differential equations (ODEs) are quite prominent in recent literature and second order initial value problems (IVPs) which falls in the family of ODEs is also a well explored area for the application of block methods. The introduction of hybrid block method methods for the solution of second order IVPs has gained good grounds in literature as the presence of off-grid points in the block method has increased the accuracy of the hybrid block methods. However, recent studies still continue to introduce new block methods that will perform more favourably than previously existing when compared in terms of error. Hence, a hybrid block method of order six is presented in this article to compete with previously existing methods of the same order and higher order. The methodology adopted in this article presents a new approach for developing the hybrid block method which is simple to implement and less computationally tiresome. The numerical results show this new \(4\)-step \(5\)-point hybrid block method performing better than previously existing methods. %9 journal article %R 10.22436/jmcs.017.04.07 %U http://dx.doi.org/10.22436/jmcs.017.04.07 %P 527-534 %0 Book %T Block methods for direct solutions of general higher order initial value problems of ordinary differential equations %A A. O. Adesanya %D 2011 %I PhD Thesis, Federal University of Technology, Akure %C Nigeria %F Adesanya2011 %0 Journal Article %T Continuous block hybrid predictor corrector method for the solution of \( y''=f(x,y,y')\) %A A. O. Adesanya %A M. R. Odekunle %J Int. J. Math. Soft Comput. %D 2012 %V 2 %F Adesanya2012 %0 Journal Article %T A new hybrid block method for the solution of general third order initial value problems of ordinary differential equations %A A. O. Adesanya %A D. M. Udoh %A A. M. Ajileye %J Int. J. Pure Appl. Math. %D 2013 %V 86 %F Adesanya2013 %0 Journal Article %T One-step implicit hybrid block method for the direct solution of general second order ordinary differential equations %A T. A. Anake %A D. O. Awoyemi %A A. O. Adesanya %J IAENG Int. J. Appl. Math. %D 2012 %V 42 %F Anake2012 %0 Journal Article %T A new eighth order implicit block algorithms for the direct solution of second order ordinary differential equations %A A. M. Badmus %J Amer. J. Comput. Math. %D 2014 %V 4 %F Badmus2014 %0 Journal Article %T Starting order seven method accurately for the solution of first initial value problems of first order ordinary differential equations %A A. A. James %A O. A. Adesanya %A K. M. Fasasi %J Progress Appl. Math. %D 2013 %V 6 %F James2013 %0 Journal Article %T A 3-step hybrid method for direct solution of second order initial value problems %A S. J. Kayode %A O. Adeyeye %J Aust. J. Basic Appl. Sci. %D 2011 %V 5 %F Kayode2011 %0 Journal Article %T Two-step two-point hybrid methods for general second order differential equations %A S. J. Kayode %A O. Adeyeye %J Afr. J. Math. Comput. Sci. Res. %D 2013 %V 6 %F Kayode2013 %0 Journal Article %T Derivation of a six-step block method for direct solution of second order ordinary differential equations %A J. O. Kuboye %A Z. Omar %J Math. Comput. Appl. %D 2015 %V 20 %F Kuboye2015 %0 Journal Article %T Direct two-point block one-step method for solving general second-order ordinary differential equations %A Z. A. Majid %A N. Z. Mokhtar %A M. Suleiman %J Math. Probl. Eng. %D 2012 %V 2012 %F Majid2012 %0 Journal Article %T A class of hybrid linear multistep methods with \(A(\alpha)\)-stability properties for stiff IVPs in ODEs %A R. I. Okuonghae %A M. N. O. Ikhile %J J. Numer. Math. %D 2013 %V 21 %F Okuonghae2013 %0 Journal Article %T A new implicit block method for solving second order ordinary differential equations directly %A Z. Omar %A J. O. Kuboye %J G.U. Journal of Science %D 2015 %V 28 %F Omar2015 %0 Journal Article %T Solving nonlinear two point boundary value problem using two step direct method %A P. S. Phang %A Z. A. Majid %A M. Suleiman %J J. Qual. Measure. Anal. %D 2011 %V 7 %F Phang2011 %0 Journal Article %T A zero-stable block method for the solution of third order ordinary differential equations %A K. Rauf %A S. A. Aniki %A S. Ibrahim %A J. O. Omolehin %J Pac. J. Sci. Tech. %D 2015 %V 16 %F Rauf2015