Learning Time Delay Systems with Neural Ordinary Differential Equations

Ji, Xunbi A.; Orosz, Gábor

doi:10.1016/j.ifacol.2022.11.337

Cited by 2 publications

(1 citation statement)

References 9 publications

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“…dy t ry t cy qt dt =+ (1.3) In this formulation, 01 q , while r and c represent parameters related to the coefficient of elasticity, spacing of lightweight springs, wire density, shock absorbers, bracing, and similar factors. Delay differential equations have been widely applied in fields like automatic control, biology, and finance [4][5][6][7][8][9][10][11][12]. This has increased scholarly interest in fractional delay differential equations, distinguishing them from their integer counterparts due to their characteristic traits of 'nonlocality' and 'memory'.…”

Section: Introductionmentioning

confidence: 99%

Generalized Legendre Polynomial Configuration Method for Solving Numerical Solutions of Fractional Pantograph Delay Differential Equations

Cui,

Feng,

Jiang

2023

J. Adv. App. Comput. Math.

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This paper develops a numerical approach for solving fractional pantograph delay differential equations using generalized Legendre polynomials. These polynomials are derived from generalized Taylor bases, which facilitate the approximation of the underlying analytical solutions, leading to the formulation of numerical solutions. The fractional pantograph delay differential equation is then transformed into a finite set of nonlinear algebraic equations using collocation points. Following this step, Newton's iterative method is applied to the resultant set of nonlinear algebraic equations to compute their numerical solutions. An error analysis for this methodology is subsequently presented, accompanied by numerical examples demonstrating its accuracy and efficiency. Overall, this study contributes a more streamlined and productive tool for determining the numerical solution of fractional differential equations.

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