Approximating a Special Class of Linear Fourth-Order Ordinary Differential Problems

  • Emilio Defez
  • Michael M. Tung
  • J. Javier Ibáñez
  • Jorge Sastre
Conference paper
Part of the Mathematics in Industry book series (MATHINDUSTRY, volume 26)


Differential matrix models are an essential ingredient of many important scientific and engineering applications. In this work, we propose a procedure to approximate the solutions of special linear fourth-order matrix differential problems of the type Y(4)(x) = A(x)Y (x) + B(x) with higher-order matrix splines. An example is included.



This work has been supported by the Spanish Ministerio de Economía y Competitividad and the European Regional Development Fund (ERDF) under grant TIN2014-59294-P.


  1. 1.
    Defez, E., Tung, M.M., Ibáñez, J., Sastre, J.: Approximating and computing nonlinear matrix differential models. Math. Comput. Model. 55(7), 2012–2022 (2012)Google Scholar
  2. 2.
    Famelis, I., Tsitouras, C.: On modifications of Runge–Kutta–Nyström methods for solving y (4) = f(x, y). Appl. Math. Comput. 273, 726–734 (2016)Google Scholar
  3. 3.
    Golub, G.H., Loan, C.F.V.: Matrix Computations, 3rd edn. The Johns Hopkins University Press, Baltimore, MD (1996)Google Scholar
  4. 4.
    Hussain, K., Ismail, F., Senu, N.: Two embedded pairs of Runge-Kutta type methods for direct solution of special fourth-order ordinary differential equations. Math. Probl. Eng. 2015 (2015). doi:10.1155/2015/196595Google Scholar
  5. 5.
    Loscalzo, F.R., Talbot, T.D.: Spline function approximations for solutions of ordinary differential equations. SIAM J. Numer. Anal. 4(3), 433–445 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Olabode, B., et al.: Implicit hybrid block Numerov-type method for the direct solution of fourth-order ordinary differential equations. Am. J. Comput. Appl. Math. 5(5), 129–139 (2015)Google Scholar
  7. 7.
    Papakostas, S.N., Tsitmidelis, S., Tsitouras, C.: Evolutionary generation of 7th order Runge - Kutta - Nyström type methods for solving y (4) = f(x, y). In: American Institute of Physics Conference Series, vol. 1702 (2015). doi: 10.1063/1.4938985

Copyright information

© Springer International Publishing AG, part of Springer Nature 2017

Authors and Affiliations

  • Emilio Defez
    • 1
  • Michael M. Tung
    • 1
  • J. Javier Ibáñez
    • 2
  • Jorge Sastre
    • 3
  1. 1.Instituto de Matemática MultidisciplinarUniversitat Politècnica de ValènciaValenciaSpain
  2. 2.Instituto de Instrumentación para Imagen MolecularUniversitat Politècnica de ValènciaValenciaSpain
  3. 3.Instituto de Telecomunicaciones y Aplicaciones MultimediaUniversitat Politècnica de ValènciaValenciaSpain

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