Analysis of an adaptive collocation solution for retarded and neutral delay systems

Maleki, Mohammad; Davari, Ali

doi:10.1007/s11075-020-01030-4

Cited by 5 publications

(3 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Wang et al (2009) show that Runge–Kutta methods based on the backward Euler method and used in conjunction with linear interpolation are contractive and asymptotically stable. Maleki and Davari (2021) present adaptive collocation methods and examine the convergence properties of the method. Recently, Mohammad and Trounev (2022) proposed the use of Euler wavelets for numerical solution of NNDEs.…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of neutral delay differential equations with high-frequency inputs

Condon

2023

COMPEL

View full text Add to dashboard Cite

Purpose The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved. Design/methodology/approach The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases. Findings An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation. Originality/value The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

show abstract

Section: Introductionmentioning

confidence: 99%

Numerical analysis of neutral delay differential equations with high-frequency inputs

Condon

2023

COMPEL

View full text Add to dashboard Cite

show abstract

“…Hence, it is crucial to develop efficient numerical techniques to simulate solutions of such equations. Many researchers reported several techniques in this development, for example, Runge-Kutta method has been used in [14], variational iteration method in [15], and other numerical schemes and properties can be found in [7,16,17].…”

Section: Introductionmentioning

confidence: 99%

A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets

Mohammad

Trounev

2022

Complexity

View full text Add to dashboard Cite

An effective numerical scheme based on Euler wavelets is proposed for numerically solving a class of neutral delay differential equations. The technique explores the numerical solution via Euler wavelet truncated series generated by a set of functions and matrix inversion of some collocation points. Based on the operational matrix, the neutral delay differential equations are reduced to a system of algebraic equations, which is solved through a numerical algorithm. The effectiveness and efficiency of the technique have been illustrated by several examples of neutral delay differential equations. The main advantages and key role of using the Euler wavelets in this work lie in the performance, accuracy, and computational cost of the proposed technique.

show abstract

“…Several studies have been done on the numerical approximations and asymptotic properties of solutions to NDDEs [1]- [7]. NDDEs have been used to develop models in engi-neering [8]- [12], biosciences [1], [13]- [17], and economics [18], [19].…”

Section: Introductionmentioning

confidence: 99%

Parameter Estimation in Neutral Delay Differential Equations Using Genetic Algorithm With Multi-Parent Crossover

Jamilla

Mendoza

2021

IEEE Access

View full text Add to dashboard Cite

Neutral delay differential equations (NDDEs) are differential equations containing time lags not only in the states but also in the state derivatives. NDDEs have applications in modeling physical and biological systems. An NDDE model may consist of several parameters, some of which can be determined using available data. Various numerical techniques have been studied to estimate parameters of mathematical models. In this study, parameter estimation is posed as an optimization problem. The use of heuristic algorithms in parameter estimation has gained popularity because of its ease of implementation, requiring only function evaluations. But to our knowledge, heuristic algorithms have never been employed in estimating parameters in NDDE models. In this work, we apply Genetic Algorithm with Multi-Parent Crossover (GA-MPC) to obtain parameter estimates of three NDDE models with a discrete delay. We compare the estimates to those obtained using standard heuristic algorithms. Results show that GA-MPC is capable of consistently identifying model parameters that provide a good fit of the model to the data.INDEX TERMS neutral delay differential equations, parameter estimation, genetic algorithm, bootstrapping, inverse problem, heuristic algorithms VOLUME x, 20xx

show abstract

Analysis of an adaptive collocation solution for retarded and neutral delay systems

Cited by 5 publications

References 40 publications

Numerical analysis of neutral delay differential equations with high-frequency inputs

Numerical analysis of neutral delay differential equations with high-frequency inputs

A New Technique for Solving Neutral Delay Differential Equations Based on Euler Wavelets

Parameter Estimation in Neutral Delay Differential Equations Using Genetic Algorithm With Multi-Parent Crossover

Contact Info

Product

Resources

About