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B. Hálková, J. Schmidt, M. Šejnoha, "Reduced Numerical Approximation of Fractional Derivative in Application to Creep", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Eighteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 10, Paper 10.1, 2025,

Keywords: springpot, fractional viscoelasticity, viscoelastic response, fractional derivative, numerical approximation of fractional derivative, reduced approximation.

Abstract

Fractional viscoelasticity offers an alternative approach to describe viscoelastic materials with the use of derivatives and integrals of non-integer order. The main disadvantage occurs in the numerical applications of this approach. Compared to standard finite-order derivatives, the numerical approximation of the fractional derivative is based on the nodal values of all previous time steps. Each of these values has a different weight when computing the next value in every subsequent step. This leads to high requirements on memory and computing time. This paper introduces several possible modifications to approximate the fractional derivative, which rely on the application of a reduced number of nodal values and thus reduce the complexity of the calculation.

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Front Page Browse CCC CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Conferences ISSN 2753-3239 CCC: 10 PROCEEDINGS OF THE EIGHTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: P. Iványi, J. Kruis and B.H.V. Topping Paper 10.1 Reduced Numerical Approximation of Fractional Derivative in Application to Creep B. Hálková, J. Schmidt and M. Šejnoha Faculty of Civil Engineering, Czech Technical University in Prague, Czech Republic Full Bibliographic Reference for this paper B. Hálková, J. Schmidt, M. Šejnoha, "Reduced Numerical Approximation of Fractional Derivative in Application to Creep", in P. Iványi, J. Kruis, B.H.V. Topping, (Editors), "Proceedings of the Eighteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Edinburgh, UK, Online volume: CCC 10, Paper 10.1, 2025, Keywords: springpot, fractional viscoelasticity, viscoelastic response, fractional derivative, numerical approximation of fractional derivative, reduced approximation. Abstract Fractional viscoelasticity offers an alternative approach to describe viscoelastic materials with the use of derivatives and integrals of non-integer order. The main disadvantage occurs in the numerical applications of this approach. Compared to standard finite-order derivatives, the numerical approximation of the fractional derivative is based on the nodal values of all previous time steps. Each of these values has a different weight when computing the next value in every subsequent step. This leads to high requirements on memory and computing time. This paper introduces several possible modifications to approximate the fractional derivative, which rely on the application of a reduced number of nodal values and thus reduce the complexity of the calculation. download the full-text of this paper (PDF, 13 pages, 613 Kb) go to the previous paper go to the next paper return to the table of contents return to the volume description
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