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Hybrid methods for direct integration of special third order ordinary differential equations

Author

Listed:
  • D. Jikantoro, Y.
  • Ismail, F.
  • Senu, N.
  • Ibrahim, Z.B.

Abstract

In this paper we present a new class of direct numerical integrators of hybrid type for special third order ordinary differential equations (ODEs), y′′′=f(x,y); namely, hybrid methods for solving third order ODEs directly (HMTD). Using the theory of B-series, order of convergence of the HMTD methods is investigated. The main result of the paper is a theorem that generates algebraic order conditions of the methods that are analogous to those of two-step hybrid method. A three-stage explicit HMTD is constructed. Results from numerical experiment suggest the superiority of the new method over several existing methods considered in the paper.

Suggested Citation

  • D. Jikantoro, Y. & Ismail, F. & Senu, N. & Ibrahim, Z.B., 2018. "Hybrid methods for direct integration of special third order ordinary differential equations," Applied Mathematics and Computation, Elsevier, vol. 320(C), pages 452-463.
    • Handle: RePEc:eee:apmaco:v:320:y:2018:i:c:p:452-463
    DOI: 10.1016/j.amc.2017.10.003
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    Cited by:

    1. Mohd Nasir, Nadirah & Abdul Majid, Zanariah & Ismail, Fudziah & Bachok, Norfifah, 2021. "Direct integration of the third-order two point and multipoint Robin type boundary value problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 182(C), pages 411-427.
    2. Reem Allogmany & Fudziah Ismail, 2020. "Implicit Three-Point Block Numerical Algorithm for Solving Third Order Initial Value Problem Directly with Applications," Mathematics, MDPI, vol. 8(10), pages 1-16, October.
    3. Michael M. Tung & Emilio Defez & Javier Ibáñez & José M. Alonso & Julia Real-Herráiz, 2022. "A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems," Mathematics, MDPI, vol. 10(16), pages 1-18, August.

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