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A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation

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  • Falcone, Alberto
  • Garro, Alfredo
  • Mukhametzhanov, Marat S.
  • Sergeyev, Yaroslav D.

Abstract

This paper is dedicated to numerical computation of higher order derivatives in Simulink. In this paper, a new module has been implemented to achieve this purpose within the Simulink-based Infinity Computer solution, recently introduced by the authors. This module offers several blocks to calculate higher order derivatives of a function given by the arithmetic operations and elementary functions. Traditionally, this can be done in Simulink using finite differences only, for which it is well-known that they can be characterized by instability and low accuracy. Moreover, the proposed module allows to calculate higher order Lie derivatives embedded in the numerical solution to Ordinary Differential Equations (ODEs). Traditionally, Simulink does not offer any practical solution for this case without using difficult external libraries and methodologies, which are domain-specific, not general-purpose and have their own limitations. The proposed differentiation module bridges this gap, is simple and does not require any additional knowledge or skills except basic knowledge of the Simulink programming language. Finally, the block for constructing the Taylor expansion of the differentiated function is also proposed, adding so another efficient numerical method for solving ODEs and for polynomial approximation of the functions. Numerical experiments on several classes of test problems confirm advantages of the proposed solution.

Suggested Citation

  • Falcone, Alberto & Garro, Alfredo & Mukhametzhanov, Marat S. & Sergeyev, Yaroslav D., 2021. "A Simulink-based software solution using the Infinity Computer methodology for higher order differentiation," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    • Handle: RePEc:eee:apmaco:v:409:y:2021:i:c:s0096300320305610
    DOI: 10.1016/j.amc.2020.125606
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    References listed on IDEAS

    as
    1. Amodio, P. & Iavernaro, F. & Mazzia, F. & Mukhametzhanov, M.S. & Sergeyev, Ya.D., 2017. "A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floating-point arithmetic," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 141(C), pages 24-39.
    2. Cococcioni, Marco & Pappalardo, Massimo & Sergeyev, Yaroslav D., 2018. "Lexicographic multi-objective linear programming using grossone methodology: Theory and algorithm," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 298-311.
    3. Renato De Leone & Giovanni Fasano & Yaroslav D. Sergeyev, 2018. "Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming," Computational Optimization and Applications, Springer, vol. 71(1), pages 73-93, September.
    4. De Leone, Renato, 2018. "Nonlinear programming and Grossone: Quadratic Programing and the role of Constraint Qualifications," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 290-297.
    5. Gaudioso, Manlio & Giallombardo, Giovanni & Mukhametzhanov, Marat, 2018. "Numerical infinitesimals in a variable metric method for convex nonsmooth optimization," Applied Mathematics and Computation, Elsevier, vol. 318(C), pages 312-320.
    6. Yaroslav D. Sergeyev & Marat S. Mukhametzhanov & Dmitri E. Kvasov & Daniela Lera, 2016. "Derivative-Free Local Tuning and Local Improvement Techniques Embedded in the Univariate Global Optimization," Journal of Optimization Theory and Applications, Springer, vol. 171(1), pages 186-208, October.
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