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Analysis of RL electric circuits modeled by fractional Riccati IVP via Jacobi-Broyden Newton algorithm

I tiakina i:
I whakaputaina i:PLoS One vol. 20, no. 1 (Jan 2025), p. e0316348
Kaituhi matua: Mahmoud Abd El-Hady
Ētahi atu kaituhi: El-Gamel, Mohamed, Homan Emadifar, El-shenawy, Atallah
I whakaputaina:
Public Library of Science
Ngā marau:
Mathematical analysis
Algorithms
Polynomials
Collocation methods
Circuits
Inductors
Error analysis
Convergence
Numerical methods
Boundary value problems
Order parameters
Partial differential equations
Smoothness
RL circuits
Computer engineering
Methods
Fractional calculus
Differential equations
Mathematical models
Ordinary differential equations
Environmental
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Whakarāpopotonga:This paper focuses on modeling Resistor-Inductor (RL) electric circuits using a fractional Riccati initial value problem (IVP) framework. Conventional models frequently neglect the complex dynamics and memory effects intrinsic to actual RL circuits. This study aims to develop a more precise representation using a fractional-order Riccati model. We present a Jacobi collocation method combined with the Jacobi-Newton algorithm to address the fractional Riccati initial value problem. This numerical method utilizes the characteristics of Jacobi polynomials to accurately approximate solutions to the nonlinear fractional differential equation. We obtain the requisite Jacobi operational matrices for the discretization of fractional derivatives, therefore converting the initial value problem into a system of algebraic equations. The convergence and precision of the proposed algorithm are meticulously evaluated by error and residual analysis. The theoretical findings demonstrate that the method attains high-order convergence rates, dependent on suitable criteria related to the fractional-order parameters and the solution’s smoothness. This study not only improves comprehension of RL circuit dynamics but also offers a solid numerical foundation for addressing intricate fractional differential equations.
ISSN:1932-6203
DOI:10.1371/journal.pone.0316348
Puna:Health & Medical Collection