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Original Articles

A new sixth-order algorithm for general second order ordinary differential equations

Pages 117-124 | Received 17 Nov 1999, Published online: 19 Mar 2007

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Read on this site (6)

S. N. Jator, A. O. Akinfenwa, S. A. Okunuga & A. B. Sofoluwe. (2013) High-order continuous third derivative formulas with block extensions for y″=f(x, y, y′). International Journal of Computer Mathematics 90:9, pages 1899-1914.
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S. N. Jator & J. Li. (2009) A self-starting linear multistep method for a direct solution of the general second-order initial value problem. International Journal of Computer Mathematics 86:5, pages 827-836.
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S. M. Mahmoud & M. Sh. Osman. (2009) On a class of spline-collocation methods for solving second-order initial-value problems. International Journal of Computer Mathematics 86:4, pages 616-630.
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D. O. Awoyemi & O. M. Idowu. (2005) A class of hybrid collocation methods for third-order ordinary differential equations. International Journal of Computer Mathematics 82:10, pages 1287-1293.
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D. O. Awoyemi. (2003) A P-Stable Linear Multistep Method For Solving General Third Order Ordinary Differential Equations. International Journal of Computer Mathematics 80:8, pages 985-991.
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Articles from other publishers (27)

Higinio Ramos, Ridwanulahi Abdulganiy, Ruth Olowe & Samuel Jator. (2021) A Family of Functionally-Fitted Third Derivative Block Falkner Methods for Solving Second-Order Initial-Value Problems with Oscillating Solutions. Mathematics 9:7, pages 713.
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Saranya Gunasingam & Amirah Azmi. Order seven block integrator method for the solution of first order ordinary differential equation. Order seven block integrator method for the solution of first order ordinary differential equation.
Ezekiel Olukunle Ojo & Okoro Felix M.. (2020) Bernstein induced one step hybrid scheme for general solution of second order initial value problems. Malaya Journal of Matematik 8:2, pages 350-355.
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S. N. Jator, F. F. Ngwane & N. O. Kirby. (2019) Functionally Fitted Block Method for Solving the General Oscillatory Second-Order Initial Value Problems and Hyperbolic Partial Differential Equations. Mathematical Problems in Engineering 2019, pages 1-14.
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Tahani Salama Mohamed, Norazak Senu, Zarina Bibi Ibrahim & Nik Mohd Asri Nik Long. (2018) Exponentially Fitted and Trigonometrically Fitted Two-Derivative Runge-Kutta-Nyström Methods for Solving . Mathematical Problems in Engineering 2018, pages 1-19.
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T. S. Mohamed, N. Senu, Z. B. Ibrahim & N. M. A. Nik Long. (2018) Efficient Two-Derivative Runge-Kutta-Nyström Methods for Solving General Second-Order Ordinary Differential Equations . Discrete Dynamics in Nature and Society 2018, pages 1-10.
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Higinio Ramos, Shubham Mehta & J. Vigo-Aguiar. (2017) A unified approach for the development of -step block Falkner-type methods for solving general second-order initial-value problems in ODEs . Journal of Computational and Applied Mathematics 318, pages 550-564.
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F. F. Ngwane & S. N. Jator. (2017) A Trigonometrically Fitted Block Method for Solving Oscillatory Second-Order Initial Value Problems and Hamiltonian Systems. International Journal of Differential Equations 2017, pages 1-14.
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J. O. Kuboye & Z. Omar. 2017. Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015). Proceedings of the International Conference on Computing, Mathematics and Statistics (iCMS 2015) 225 233 .
S. N. Jator. (2015) Block third derivative method based on trigonometric polynomials for periodic initial-value problems. Afrika Matematika 27:3-4, pages 365-377.
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Nazreen Waeleh & Zanariah Abdul Majid. (2016) A 4-Point Block Method for Solving Higher Order Ordinary Differential Equations Directly. International Journal of Mathematics and Mathematical Sciences 2016, pages 1-8.
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Lee Ken Yap & Fudziah Ismail. Ninth order block hybrid collocation method for second order ordinary differential equations. Ninth order block hybrid collocation method for second order ordinary differential equations.
S. N. Jator. (2014) Implicit third derivative Runge-Kutta-Nyström method with trigonometric coefficients. Numerical Algorithms 70:1, pages 133-150.
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Kasim Hussain, Fudziah Ismail & Norazak Senu. (2015) Runge-Kutta Type Methods for Directly Solving Special Fourth-Order Ordinary Differential Equations. Mathematical Problems in Engineering 2015, pages 1-11.
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F. F. Ngwane & S. N. Jator. (2015) Solving the Telegraph and Oscillatory Differential Equations by a Block Hybrid Trigonometrically Fitted Algorithm. International Journal of Differential Equations 2015, pages 1-15.
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Samuel N Jator & Leong Lee. (2014) Implementing a seventh-order linear multistep method in a predictor-corrector mode or block mode: which is more efficient for the general second order initial value problem. SpringerPlus 3:1.
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Mathew Remilekun Odekunle, Michael Otokpa Egwurube, Adetola Olaide Adesanya & Mfon Okon Udo. (2014) Five Steps Block Predictor-Block Corrector Method for the Solution of <i>y''</i> = <i>f</i> (<i>x</i>,<i>y</i>,<i>y'</i>). Applied Mathematics 05:08, pages 1252-1266.
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Xiong You & Zhaoxia Chen. (2013) Direct integrators of Runge–Kutta type for special third-order ordinary differential equations. Applied Numerical Mathematics 74, pages 128-150.
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Adetola Olaide Adesanya, Mattew Remilekun Odekunle & Mfon Odo Udoh. (2013) Four Steps Continuous Method for the Solution of <i>y″</i>= <i>f</i> (<i>x, y, y′</i>). American Journal of Computational Mathematics 03:02, pages 169-174.
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Samuel N. Jator, S. Swindell & R. French. (2012) Trigonometrically fitted block Numerov type method for y′′ = f(x, y, y′). Numerical Algorithms 62:1, pages 13-26.
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S.N. Jator. (2012) A continuous two-step method of order 8 with a block extension for. Applied Mathematics and Computation 219:3, pages 781-791.
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S. Mehrkanoon, T. Falck & J. A. K. Suykens. (2012) Approximate Solutions to Ordinary Differential Equations Using Least Squares Support Vector Machines. IEEE Transactions on Neural Networks and Learning Systems 23:9, pages 1356-1367.
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Samuel N. Jator & Jiang Li. (2011) An algorithm for second order initial and boundary value problems with an automatic error estimate based on a third derivative method. Numerical Algorithms 59:3, pages 333-346.
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Siamak Mehrkanoon. (2010) A direct variable step block multistep method for solving general third-order ODEs. Numerical Algorithms 57:1, pages 53-66.
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A. H. Bhrawy & W. M. Abd-Elhameed. (2011) New Algorithm for the Numerical Solutions of Nonlinear Third-Order Differential Equations Using Jacobi-Gauss Collocation Method. Mathematical Problems in Engineering 2011, pages 1-14.
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S.N. Jator. (2010) Solving second order initial value problems by a hybrid multistep method without predictors. Applied Mathematics and Computation 217:8, pages 4036-4046.
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S. J. Kayode. (2008) An Efficient Zero-Stable Numerical Method for Fourth-Order Differential Equations. International Journal of Mathematics and Mathematical Sciences 2008, pages 1-10.
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