Numerical solution of singularly perturbed delay differential equations using gaussion quadrature method

Phaneendra, K.; Lalu, M.

doi:10.1088/1742-6596/1344/1/012013

Cited by 7 publications

(4 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Te solution to the problem is utilized by a hybrid diference method that lies on a Shishkin-type mesh. Te interior and boundary layer occurs in the exact solution because of the delay term [43,44].…”

Section: Introductionmentioning

confidence: 99%

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Ahmad,

Hussain,

Ilyas

et al. 2023

International Journal of Intelligent Systems

View full text Add to dashboard Cite

The proposed research utilizes a computational approach to attain a numerical solution for the singularly perturbed delay differential equation (SPDDE) problem arising in the neuronal variability model through artificial neural networks (ANNs) with different solvers. The log-sigmoid function is used to construct the fitness function. The implementation of ANN on SPDDE problems is formulated for different solvers and trained with different weights. The optimization solvers such as the genetic algorithm (GA), sequential quadratic programming (SQP), and pattern search (PS) are hybridized with the active set technique (AST) and the interior-point technique (IPT) and is used to check the accuracy and rapid convergence of the numerical results of the SPDDE model. The numerical outcomes demonstrate that the system is easy to handle and efficient to solve with boundary conditions. Moreover, we used the mean residual error for one hundred runs for each solver to validate the accuracy of the proposed scheme.

show abstract

Section: Introductionmentioning

confidence: 99%

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Ahmad,

Hussain,

Ilyas

et al. 2023

International Journal of Intelligent Systems

View full text Add to dashboard Cite

show abstract

“…They developed a mathematical model by random synaptic inputs in dendrites for estimating the approximate time for the activation of action potentials in nerve cells and also discussed issues with solutions that had rapid oscillations in their study. The authors of [16] utilized a quadrature method for solving the SPDE, as well as a two-point quadrature rule to obtain a tridiagonal system. The authors in [17] developed a finite difference approach for solving SPDEs with turning points and mixed shifts.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Singularly Perturbed Delay Differential Equations With Large Delay Using an Exponential Spline

Omkar¹,

Phaneendra²

2022

Int. J. Anal. Appl.

View full text Add to dashboard Cite

In this study, numerical solution of a differential-difference equation with a boundary layer at one end of the domain is suggested using an exponential spline. The numerical scheme is developed using an exponential spline with a special type of mesh. A fitting parameter is inserted in the scheme to improve the accuracy and to control the oscillations in the solution due to large delay. Convergence of the method is examined. The error profiles are represented by tabulating the maximum absolute errors in the solution. Graphs are being used to show that how the fitting parameter influence the layer structure.

show abstract

“…In [2] Bahgat and Hafiz used Taylor's series approximation for the delay terms and applied fifth and sixth order finite difference approximation for the derivative terms and developed a finite difference scheme. In [15] Phaneendra and Lulu used a Gaussian quadrature integration method with an exponential fitting parameter. In [17] Ranjan and Prasad developed a FDM using an exponentially fitted finite difference method.…”

Section: Introductionmentioning

confidence: 99%

Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays

Woldaregay

Aniley

Duressa

2021

Theor appl mech (Belgr)

View full text Add to dashboard Cite

This paper deals with solution methods for singularly perturbed delay differential equations having delay on the convection and reaction terms. The considered problem exhibits an exponential boundary layer on the left or right side of the domain. The terms with the delay are treated using Taylor?s series approximation and the resulting singularly perturbed boundary value problem is solved using a specially designed exponentially finite difference method. The stability of the scheme is analysed and investigated using a comparison principle and solution bound. The formulated scheme converges uniformly with linear order of convergence. The theoretical findings are validated using three numerical test examples.

show abstract

Numerical solution of singularly perturbed delay differential equations using gaussion quadrature method

Cited by 7 publications

References 5 publications

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Integrated Stochastic Investigation of Singularly Perturbed Delay Differential Equations for the Neuronal Variability Model

Numerical Simulation of Singularly Perturbed Delay Differential Equations With Large Delay Using an Exponential Spline

Fitted numerical scheme for singularly perturbed convection-diffusion reaction problems involving delays

Contact Info

Product

Resources

About