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On the use of a high-order spectral method and the geometric progression for the analysis of stationary bifurcation of nonlinear problems

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Abstract

In this research, we suggest employing red high-order meshless geometric progression technique to numerically explore stable bifurcation points and bifurcated branches. We proposed to use a high-order approach (HOA) for the solution of nonlinear problems. The proposed approach combines the asymptotic continuation technique and a discretization carried out using the quadratic spectral method. The governing equations are presented under a strong nonlinear formulation. The nonlinear equations are converted into a series of linear equations thanks to the high-order meshless approach (HOA). This method enables the precise detection of the bifurcation locations. A resolution strategy aims to handle bifurcation events for biharmonic problems by expanding in various geometries, where the stable issue becomes unstable after a critical point. The acquired findings are contrasted with those reported in the literature and with those computed using the high-order finite element approach coupled with geometric progression.

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Data Availability

The data that support the findings of this study are available from the corresponding author, upon reasonable request.

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Authors and Affiliations

  1. LAMSAD Laboratory, Ecole National des Sciences Appliqués, Hassan First University of Settat, 26100, Berrechid, Morocco

    Mohamed Drissi & Mohamed Mansouri

  2. LISA Laboratory, Ecole National des Sciences Appliqués, Hassan First University of Settat, 26100, Berrechid, Morocco

    Said Mesmoudi

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  1. Mohamed Drissi
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  2. Said Mesmoudi
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Drissi, M., Mesmoudi, S. & Mansouri, M. On the use of a high-order spectral method and the geometric progression for the analysis of stationary bifurcation of nonlinear problems. Int. J. Dynam. Control 11, 2633–2643 (2023). https://doi.org/10.1007/s40435-023-01141-5

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