A novel numerical scheme for fractional differential equations using extreme learning machine

Sivalingam S M, Pushpendra Kumar and V. Govindaraj

Physica A: Statistical Mechanics and its Applications, 2023, vol. 622, issue C

Abstract: In this paper, we propose a neural network-based approach with an Extreme Learning Machine (ELM) for solving fractional differential equations. The solution procedure for the linear and nonlinear fractional differential equations has been derived. Also the convergence and stability of the proposed method is provided. Then we examine the numerical solution of several fractional-order ordinary and partial differential equations. As a last example the Burgers equation without an explicit exact solution. The effect of changing the number of neurons on the accuracy of the solution is obtained graphically.

Keywords: Extreme learning machine; Neural networks; Legendre polynomials; Operational matrix (search for similar items in EconPapers)
Date: 2023
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:622:y:2023:i:c:s0378437123004429

DOI: 10.1016/j.physa.2023.128887

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