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A Matrix Spline Method for a Class of Fourth-Order Ordinary Differential Problems

Author

Listed:
  • Michael M. Tung

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Emilio Defez

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Javier Ibáñez

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • José M. Alonso

    (Instituto de Instrumentación Para Imagen Molecular, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

  • Julia Real-Herráiz

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain)

Abstract

Differential matrix models provide an elementary blueprint for the adequate and efficient treatment of many important applications in science and engineering. In the present work, we suggest a procedure, extending our previous research results, to represent the solutions of nonlinear matrix differential problems of fourth order given in the form Y ( 4 ) ( x ) = f ( x , Y ( x ) ) in terms of higher-order matrix splines. The corresponding algorithm is explained, and some numerical examples for the illustration of the method are included.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:16:p:2826-:d:883530
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    References listed on IDEAS

    as
    1. 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.
    2. A. K. Alomari & N. Ratib Anakira & A. Sami Bataineh & I. Hashim, 2013. "Approximate Solution of Nonlinear System of BVP Arising in Fluid Flow Problem," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-7, May.
    3. 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, Hindawi, vol. 2015, pages 1-12, December.
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