Hermite collocation method for obtaining the chaotic behavior of a nonlinear coupled system of FDEs

M. M. Khader and Mohammed M. Babatin
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M. M. Khader: Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia†Department of Mathematics, Faculty of Science, Benha University, Benha, Egypt
Mohammed M. Babatin: Department of Mathematics and Statistics, College of Science, Imam Mohammad, Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia

International Journal of Modern Physics C (IJMPC), 2020, vol. 31, issue 07, 1-12

Abstract: This paper is devoted to introduce an efficient solver using the Hermite collocation technique (HCT), of the coupled system of fractional differential equations (FDEs). The given systems are of basic importance in modeling various phenomena like Cascades and Compartment Analysis, Pond Pollution, Home Heating, Chemostats, and Microorganism Culturing, Nutrient Flow in an Aquarium, Biomass Transfer, Forecasting Prices, Electrical Network, Earthquake Effects on Buildings. The proposed method reduces the system of FDEs to a system of algebraic equations in the coefficients of the expansion using the Hermite polynomials. The introduced method is computer oriented and provides highly accurate solution. To demonstrate the efficiency of the method, two examples are solved and the results are displayed graphically. Finally, we convert the presented coupled systems from the case of its standard form to a first-order ordinary differential equations to compare the obtained numerical solutions with those solutions using the fourth-order Runge–Kutta method (RK4).

Keywords: Coupled system of fractional differential equations; Caputo fractional derivative; Hermite collocation technique; fourth-order Runge–Kutta method (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1142/S012918312050093X

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