TY - JOUR AU - Oluwaseun, Adeyeye PY - 2017 TI - \(4\)-step \(5\)-point hybrid block method for the direct solution of second order initial value problems JO - Journal of Mathematics and Computer Science SP - 527-534 VL - 17 IS - 4 AB - 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. SN - ISSN 2008-949X UR - http://dx.doi.org/10.22436/jmcs.017.04.07 DO - 10.22436/jmcs.017.04.07 ID - Oluwaseun2017 ER - TY - BOOK TI - Block methods for direct solutions of general higher order initial value problems of ordinary differential equations AU - A. O. Adesanya PB - PhD Thesis, Federal University of Technology, Akure PY - 2011 DA - 2011// CY - Nigeria ID - Adesanya2011 ER - TY - JOUR TI - Continuous block hybrid predictor corrector method for the solution of \( y''=f(x,y,y')\) AU - A. O. Adesanya AU - M. R. Odekunle JO - Int. J. Math. Soft Comput. PY - 2012 DA - 2012// VL - 2 ID - Adesanya2012 ER - TY - JOUR TI - A new hybrid block method for the solution of general third order initial value problems of ordinary differential equations AU - A. O. Adesanya AU - D. M. Udoh AU - A. M. Ajileye JO - Int. J. Pure Appl. Math. PY - 2013 DA - 2013// VL - 86 ID - Adesanya2013 ER - TY - JOUR TI - One-step implicit hybrid block method for the direct solution of general second order ordinary differential equations AU - T. A. Anake AU - D. O. Awoyemi AU - A. O. Adesanya JO - IAENG Int. J. Appl. Math. PY - 2012 DA - 2012// VL - 42 ID - Anake2012 ER - TY - JOUR TI - A new eighth order implicit block algorithms for the direct solution of second order ordinary differential equations AU - A. M. Badmus JO - Amer. J. Comput. Math. PY - 2014 DA - 2014// VL - 4 ID - Badmus2014 ER - TY - JOUR TI - Starting order seven method accurately for the solution of first initial value problems of first order ordinary differential equations AU - A. A. James AU - O. A. Adesanya AU - K. M. Fasasi JO - Progress Appl. Math. PY - 2013 DA - 2013// VL - 6 ID - James2013 ER - TY - JOUR TI - A 3-step hybrid method for direct solution of second order initial value problems AU - S. J. Kayode AU - O. Adeyeye JO - Aust. J. Basic Appl. Sci. PY - 2011 DA - 2011// VL - 5 ID - Kayode2011 ER - TY - JOUR TI - Two-step two-point hybrid methods for general second order differential equations AU - S. J. Kayode AU - O. Adeyeye JO - Afr. J. Math. Comput. Sci. Res. PY - 2013 DA - 2013// VL - 6 ID - Kayode2013 ER - TY - JOUR TI - Derivation of a six-step block method for direct solution of second order ordinary differential equations AU - J. O. Kuboye AU - Z. Omar JO - Math. Comput. Appl. PY - 2015 DA - 2015// VL - 20 ID - Kuboye2015 ER - TY - JOUR TI - Direct two-point block one-step method for solving general second-order ordinary differential equations AU - Z. A. Majid AU - N. Z. Mokhtar AU - M. Suleiman JO - Math. Probl. Eng. PY - 2012 DA - 2012 // VL - 2012 ID - Majid2012 ER - TY - JOUR TI - A class of hybrid linear multistep methods with \(A(\alpha)\)-stability properties for stiff IVPs in ODEs AU - R. I. Okuonghae AU - M. N. O. Ikhile JO - J. Numer. Math. PY - 2013 DA - 2013// VL - 21 ID - Okuonghae2013 ER - TY - JOUR TI - A new implicit block method for solving second order ordinary differential equations directly AU - Z. Omar AU - J. O. Kuboye JO - G.U. Journal of Science PY - 2015 DA - 2015// VL - 28 ID - Omar2015 ER - TY - JOUR TI - Solving nonlinear two point boundary value problem using two step direct method AU - P. S. Phang AU - Z. A. Majid AU - M. Suleiman JO - J. Qual. Measure. Anal. PY - 2011 DA - 2011// VL - 7 ID - Phang2011 ER - TY - JOUR TI - A zero-stable block method for the solution of third order ordinary differential equations AU - K. Rauf AU - S. A. Aniki AU - S. Ibrahim AU - J. O. Omolehin JO - Pac. J. Sci. Tech. PY - 2015 DA - 2015// VL - 16 ID - Rauf2015 ER -