Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models

İbrahim Avcı

doi:10.53391/mmnsa.1428035

EN

Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models

Abstract

In this paper, we introduce a pioneering numerical technique that combines generalized Laguerre polynomials with an operational matrix of fractional integration to address fractional models in electrical circuits. Specifically focusing on Resistor-Inductor ($RL$), Resistor-Capacitor ($RC$), Resonant (Inductor-Capacitor) ($LC$), and Resistor-Inductor-Capacitor ($RLC$) circuits within the framework of the Caputo derivative, our approach aims to enhance the accuracy of numerical solutions. We meticulously construct an operational matrix of fractional integration tailored to the generalized Laguerre basis vector, facilitating a transformation of the original fractional differential equations into a system of linear algebraic equations. By solving this system, we obtain a highly accurate approximate solution for the electrical circuit model under consideration. To validate the precision of our proposed method, we conduct a thorough comparative analysis, benchmarking our results against alternative numerical techniques reported in the literature and exact solutions where available. The numerical examples presented in our study substantiate the superior accuracy and reliability of our generalized Laguerre-enhanced operational matrix collocation method in effectively solving fractional electrical circuit models.

Keywords

numerical analysis, electrical circuits, generalized Laguerre polynomials, fractional integrals, fractional derivatives

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Details

Primary Language

English

Subjects

Numerical Solution of Differential and Integral Equations, Numerical Analysis, Numerical and Computational Mathematics (Other), Applied Mathematics (Other)

Journal Section

Research Article

Authors

İbrahim Avcı ^*
0000-0003-0986-2195
Kuzey Kıbrıs Türk Cumhuriyeti

Publication Date

March 31, 2024

Submission Date

January 29, 2024

Acceptance Date

March 31, 2024

Published in Issue

Year 2024 Volume: 4 Number: 1

DOI

https://doi.org/10.53391/mmnsa.1428035

IZ

https://izlik.org/JA78FF59UN

APA

Avcı, İ. (2024). Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models. Mathematical Modelling and Numerical Simulation With Applications, 4(1), 110-132. https://doi.org/10.53391/mmnsa.1428035

AMA

1.Avcı İ. Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models. MMNSA. 2024;4(1):110-132. doi:10.53391/mmnsa.1428035

Chicago

Avcı, İbrahim. 2024. “Spectral Collocation With Generalized Laguerre Operational Matrix for Numerical Solutions of Fractional Electrical Circuit Models”. Mathematical Modelling and Numerical Simulation With Applications 4 (1): 110-32. https://doi.org/10.53391/mmnsa.1428035.

EndNote

Avcı İ (March 1, 2024) Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models. Mathematical Modelling and Numerical Simulation with Applications 4 1 110–132.

IEEE

[1]İ. Avcı, “Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models”, MMNSA, vol. 4, no. 1, pp. 110–132, Mar. 2024, doi: 10.53391/mmnsa.1428035.

ISNAD

Avcı, İbrahim. “Spectral Collocation With Generalized Laguerre Operational Matrix for Numerical Solutions of Fractional Electrical Circuit Models”. Mathematical Modelling and Numerical Simulation with Applications 4/1 (March 1, 2024): 110-132. https://doi.org/10.53391/mmnsa.1428035.

JAMA

1.Avcı İ. Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models. MMNSA. 2024;4:110–132.

MLA

Avcı, İbrahim. “Spectral Collocation With Generalized Laguerre Operational Matrix for Numerical Solutions of Fractional Electrical Circuit Models”. Mathematical Modelling and Numerical Simulation With Applications, vol. 4, no. 1, Mar. 2024, pp. 110-32, doi:10.53391/mmnsa.1428035.

Vancouver

1.İbrahim Avcı. Spectral collocation with generalized Laguerre operational matrix for numerical solutions of fractional electrical circuit models. MMNSA. 2024 Mar. 1;4(1):110-32. doi:10.53391/mmnsa.1428035

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