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International Journal of Computer Mathematics Volume 82, 2005 - Issue 10
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Original Articles

A class of hybrid collocation methods for third-order ordinary differential equations

D. O. Awoyemi Department of Industrial Mathematics, Federal University of Technology, Akure, NigeriaCorrespondence[email protected]
&
O. M. Idowu Department of Industrial Mathematics, Federal University of Technology, Akure, Nigeria
Pages 1287-1293 | Received 11 Aug 2004, Published online: 19 Aug 2006

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Mohamed Salah, Ola Ragb & Abdul-Majid Wazwaz. (2022) Efficient discrete singular convolution differential quadrature algorithm for solitary wave solutions for higher dimensions in shallow water waves. Waves in Random and Complex Media 0:0, pages 1-18.
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A. Boutayeb & A. Chetouani. (2007) A mini-review of numerical methods for high-order problems† . International Journal of Computer Mathematics 84:4, pages 563-579.
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Junaid Ahmad, Muhammad Arshad, Aftab Hussain & Hamed Al Sulami. (2023) A Green’s Function Based Iterative Approach for Solutions of BVPs in Symmetric Spaces. Symmetry 15:10, pages 1838.
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Ezekiel Olaoluwa Omole, Emmanuel Oluseye Adeyefa, Victoria Iyadunni Ayodele, Ali Shokri & Yuanheng Wang. (2023) Ninth-order Multistep Collocation Formulas for Solving Models of PDEs Arising in Fluid Dynamics: Design and Implementation Strategies. Axioms 12:9, pages 891.
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Richard Olatokunbo Akinola, Ali Shokri, Shao-Wen Yao & Stephen Yakubu Kutchin. (2022) Circumventing Ill-Conditioning Arising from Using Linear Multistep Methods in Approximating the Solution of Initial Value Problems. Mathematics 10:16, pages 2910.
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Firas A. Fawzi, Zeyad M. Abdullah & Nazar K. Hussein. (2021) Two Embedded Pairs for Solve Directly Third-Order Ordinary Differential Equation by Using Runge-Kutta Type Method (RKTGD). Journal of Physics: Conference Series 1879:2, pages 022123.
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Mahboub Baccouch. (2021) The discontinuous Galerkin method for general nonlinear third-order ordinary differential equations. Applied Numerical Mathematics 162, pages 331-350.
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Rida Malik, Faheem Khan, Muhammad Basit, Abdul Ghaffar, Kottakkaran Sooppy Nisar, Emad E. Mahmoud & Masnour S.M. Lotayif. (2021) Bernstein basis functions based algorithm for solving system of third order initial value problems. Alexandria Engineering Journal 60:2, pages 2395-2404.
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Mukaddes Ökten Turacı & Merve Özdemir. (2020) A sixth‐order improved Runge–Kutta direct method for special third‐order ordinary differential equations . Numerical Methods for Partial Differential Equations 37:2, pages 987-997.
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Sana’a Nazmi Khataybeh, Ishak Hashim & Mohammed Alshbool. (2019) Solving directly third-order ODEs using operational matrices of Bernstein polynomials method with applications to fluid flow equations. Journal of King Saud University - Science 31:4, pages 822-826.
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Nizam Ghawadri, Norazak Senu, Firas Fawzi, Fudziah Ismail & Zarina Ibrahim. (2019) Explicit Integrator of Runge-Kutta Type for Direct Solution of u(4)=f(x,u,u′,u′′). Symmetry 11:2, pages 246.
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Y. D. Jikantoro, F. Ismail, N. Senu & Z.B. Ibrahim. (2018) Hybrid methods for direct integration of special third order ordinary differential equations. Applied Mathematics and Computation 320, pages 452-463.
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Y. D. Jikantoro, F. Ismail, N. Senu & Z. B. Ibrahim. (2018) A New Integrator for Special Third Order Differential Equations With Application to Thin Film Flow Problem. Indian Journal of Pure and Applied Mathematics 49:1, pages 151-167.
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Lee Ken Yap & Fudziah Ismail. Four point block hybrid collocation method for direct solution of third order ordinary differential equations. Four point block hybrid collocation method for direct solution of third order ordinary differential equations.
S. N. Khataybeh & I. Hashim. On method of solving third-order ordinary differential equations directly using Bernstein polynomials. On method of solving third-order ordinary differential equations directly using Bernstein polynomials.
Kasim Abbas Hussain, Fudziah Ismail, Norazak Senu & Faranak Rabiei. (2017) Fourth-Order Improved Runge–Kutta Method for Directly Solving Special Third-Order Ordinary Differential Equations. Iranian Journal of Science and Technology, Transactions A: Science 41:2, pages 429-437.
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Mohamed A. Ramadan, Kamal R. Raslan, Talaat S. El Danaf & Mohamed A. Abd El Salam. (2017) An exponential Chebyshev second kind approximation for solving high-order ordinary differential equations in unbounded domains, with application to Dawson's integral. Journal of the Egyptian Mathematical Society 25:2, pages 197-205.
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N. A. Ahmad, N. Senu & F. Ismail. (2017) Phase-Fitted and Amplification-Fitted Higher Order Two-Derivative Runge-Kutta Method for the Numerical Solution of Orbital and Related Periodical IVPs. Mathematical Problems in Engineering 2017, pages 1-11.
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Kasim Hussain, Fudziah Ismail & Norazak Senu. (2016) Solving directly special fourth-order ordinary differential equations using Runge–Kutta type method. Journal of Computational and Applied Mathematics 306, pages 179-199.
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Marzieh Rajabi, Fudziah Ismail & Norazak Senu. Linear 3 and 5-step methods using Taylor series expansion for solving special 3rd order ODEs. Linear 3 and 5-step methods using Taylor series expansion for solving special 3rd order ODEs.
Mariam Abushammala, S.A. Khuri & A. Sayfy. (2015) A novel fixed point iteration method for the solution of third order boundary value problems. Applied Mathematics and Computation 271, pages 131-141.
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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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Kasim Hussain, Fudziah Ismail & Norazak Senu. (2015) Two Embedded Pairs of Runge-Kutta Type Methods for Direct Solution of Special Fourth-Order Ordinary Differential Equations. Mathematical Problems in Engineering 2015, pages 1-12.
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N. Senu, M. Mechee, F. Ismail & Z. Siri. (2014) Embedded explicit Runge–Kutta type methods for directly solving special third order differential equations. Applied Mathematics and Computation 240, pages 281-293.
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Mohammed S. Mechee, F. Ismail, Z. Siri & N. Senu. (2014) A Third-Order Direct Integrators of Runge-Kutta Type for Special Third-Order Ordinary and Delay Differential Equations. Asian Journal of Applied Sciences 7:3, pages 102-116.
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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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Lee Ken Yap, Fudziah Ismail & Norazak Senu. (2014) An Accurate Block Hybrid Collocation Method for Third Order Ordinary Differential Equations. Journal of Applied Mathematics 2014, pages 1-9.
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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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M. Mechee, N. Senu, F. Ismail, B. Nikouravan & Z. Siri. (2013) A Three-Stage Fifth-Order Runge-Kutta Method for Directly Solving Special Third-Order Differential Equation with Application to Thin Film Flow Problem. Mathematical Problems in Engineering 2013, pages 1-7.
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Adetola O. Adesanya, Mfon O. Udo & Adam M. Alkali. (2012) A New Block-Predictor Corrector Algorithm for the Solution of y’’’=f(x, y, y’, y’’). American Journal of Computational Mathematics 02:04, pages 341-344.
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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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Kayode. (2010) A Multiderivative Collocation Method for 5th Order Ordinary Differential Equations. Journal of Mathematics and Statistics 6:1, pages 60-63.
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