Direct Integrators for the General Third-Order Ordinary Differential Equations with an Application to the Korteweg–de Vries Equation

  • Samuel JatorEmail author
  • Temitayo Okunlola
  • Toheeb Biala
  • Raphael Adeniyi
Original Paper


We construct a new class of implicit continuous linear multistep methods (LMMs) which are used as boundary value methods for the numerical integration of the general third order initial and boundary value problems in ordinary differential equations, including the Korteweg–de Vries equation. The boundary value methods obtained from these continuous LMMs are weighted the same and are used to simultaneously generate approximate solutions to the exact solutions in the entire interval of integration. We established the convergence analysis of the methods and several numerical examples are given to show the performance of the methods.


Boundary value methods Third order problems Convergence Linear multistep methods Korteweg–de Vries equation 

Mathematics Subject Classification

65L05 65L06 65L10 65L12 



The authors are very grateful to the referee whose valuable suggestions greatly improved the manuscript.


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Copyright information

© Springer Nature India Private Limited 2018

Authors and Affiliations

  • Samuel Jator
    • 1
    Email author
  • Temitayo Okunlola
    • 2
  • Toheeb Biala
    • 3
  • Raphael Adeniyi
    • 4
  1. 1.Department of Mathematics and StatisticsAustin Peay State UniversityClarksvilleUSA
  2. 2.Department of Physical and Mathematical ScienceAfe Babalola UniversityAdo EkitiNigeria
  3. 3.Department of Mathematics and Computer ScienceJigawa State UniversityKafin HausaNigeria
  4. 4.Department of MathematicsUniversity of IlorinIlorinNigeria

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