A Second Order Stabilized Central Difference Method for Singularly Perturbed Differential Equations with a Large Negative Shift

Kumar, Narendra; Rao, R. Nageshwar

doi:10.1007/s12591-020-00532-w

Cited by 10 publications

(6 citation statements)

References 29 publications

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“…Three examples of the scheme with the right end boundary layer are provided. The maximum absolute errors (MAEs) in the solutions are tabulated in Tables 1, 2 and 3 in comparison to the method given in [27]. The rate of convergence in the solutions is also computed.…”

Section: Discussionmentioning

confidence: 99%

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

Srinivas,

Phaneendra

2024

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A trigonometric spline based computational technique is suggested for the numerical solution of layer behavior differential-difference equations with a fixed large delay. The continuity of the first order derivative of the trigonometric spline at the interior mesh point is used to develop the system of difference equations. With the help of singular perturbation theory, a fitting parameter is inserted into the difference scheme to minimize the error in the solution. The method is examined for convergence. We have also discussed the impact of shift or delay on the boundary layer. The maximum absolute errors in comparison to other approaches in the literature are tallied, and layer behavior is displayed in graphs, to demonstrate the feasibility of the suggested numerical method.

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Section: Discussionmentioning

confidence: 99%

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

Srinivas,

Phaneendra

2024

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“…To provide the convergence analysis of the proposed numerical scheme, we follow the approaches in [29,30]. From (19a), we have a system of equations as…”

Section: Convergence Analysismentioning

confidence: 99%

An Exponentially Fitted Numerical Scheme via Domain Decomposition for Solving Singularly Perturbed Differential Equations with Large Negative Shift

Ejere

Duressa

Woldaregay

et al. 2022

Journal of Mathematics

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In this study, we focus on the formulation and analysis of an exponentially fitted numerical scheme by decomposing the domain into subdomains to solve singularly perturbed differential equations with large negative shift. The solution of problem exhibits twin boundary layers due to the presence of the perturbation parameter and strong interior layer due to the large negative shift. The original domain is divided into six subdomains, such as two boundary layer regions, two interior (interfacing) layer regions, and two regular regions. Constructing an exponentially fitted numerical scheme on each boundary and interior layer subdomains and combining with the solutions on the regular subdomains, we obtain a second order ε -uniformly convergent numerical scheme. To demonstrate the theoretical results, numerical examples are provided and analyzed.

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“…A review on the solution methodology of these kind of problems is given in [23]. Kumar and Rao [24] considered a stabilized central difference method by modifying the error terms for the boundary value problem (BVP) of singularly perturbed differential equations with a large delay. The work in [25] suggested a non polynomial spline method for solving this type of problems.…”

Section: Introductionmentioning

confidence: 99%

Singular Perturbations and Large Time Delays Through Accelerated Spline-Based Compression Technique

Mariya Regal,

Kumar S

2024

Contemp. Math.

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In the quest to solve the singularly perturbed delay differential equations (SPDDEs) involving large delay with integral boundary condition, the cubic spline in compression technique is explored for the study of dynamical systems to capture complex temporal phenomena in a wide range of scientific disciplines. The integral boundary condition is handled using Simpson's 1/3 rule and the scheme's applicability is validated by numerically experimenting with some problems at different values of mesh size and perturbation parameter. Numerical data are tabulated to show that the suggested approach is more accurate and is an improvement over the methods used in the literature. The insights gained from this research paper provide a foundation for further exploration and utilization of SPDDEs in understanding and predicting the behavior of complex systems across diverse scientific domains.

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A Second Order Stabilized Central Difference Method for Singularly Perturbed Differential Equations with a Large Negative Shift

Cited by 10 publications

References 29 publications

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

A Novel Numerical Scheme for a Class of Singularly Perturbed Differential-Difference Equations with a Fixed Large Delay

An Exponentially Fitted Numerical Scheme via Domain Decomposition for Solving Singularly Perturbed Differential Equations with Large Negative Shift

Singular Perturbations and Large Time Delays Through Accelerated Spline-Based Compression Technique

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