Mixed finite difference method for singularly perturbed differential difference equations with mixed shifts via domain decomposition

Sirisha, Lakshmi; Phaneendra, K.; Reddy, Y. N.

doi:10.1016/j.asej.2016.03.009

Cited by 16 publications

(5 citation statements)

References 13 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The author suggested successive complementary expansion method (SCEM) for solving this model in [19]. A mixed FDM is proposed to solve SPDDEs with both the shifts delay and advanced in [24].…”

Section: Introductionmentioning

confidence: 99%

Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

Ragula¹,

Soujanya²,

Swarnakar³

2023

Int. J. Anal. Appl.

View full text Add to dashboard Cite

In this paper, a second order singularly perturbed differential difference equation with both the negative and positive shifts is considered. A fitted non-polynomial spline approach is applied to solve the problem. Taylor series expansion process is being used to produce an approximated form of the considered problem, and then a fitted non-polynomial spline approach is devised in the form of a three-term recurrence relation. The convergence of the method is examined, and a quadratic rate of convergence is achieved. The maximum absolute error with quadratic rate of convergence of the solution is recorded. Layer profile is examined using the graphs.

show abstract

Section: Introductionmentioning

confidence: 99%

Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

Ragula¹,

Soujanya²,

Swarnakar³

2023

Int. J. Anal. Appl.

View full text Add to dashboard Cite

show abstract

“…The authors in [9] used a nonpolynomial spline to develop a numerical solution for a DDEs having layer with a small and large delay in the differentiated terms. Using domain decomposition, the authors of [10] suggested a mixed difference technique to solve DDEs with mixed shifts. For a class of linear second-order DDE type, Lange and Miura [11,12] developed an asymptotic method.…”

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

“…Sirisha et al [20] addressed the mixed shifts problem by decomposing the domain and applying a mixed difference technique. Phaneendra et.…”

Section: Introductionmentioning

confidence: 99%

Difference Scheme for Differential-Difference Problems with Small Shifts Arising in Computational Model of Neuronal Variability

Kodipaka¹,

Emineni

Phaneendra

2022

International Journal of Applied Mechanics and Engineering

View full text Add to dashboard Cite

The solution of differential-difference equations with small shifts having layer behaviour is the subject of this study. A difference scheme is proposed to solve this equation using a non-uniform grid. With the non-uniform grid, finite - difference estimates are derived for the first and second-order derivatives. Using these approximations, the given equation is discretized. The discretized equation is solved using the tridiagonal system algorithm. Convergence of the scheme is examined. Various numerical simulations are presented to demonstrate the validity of the scheme. In contrast to other techniques, maximum errors in the solution are organized to support the method. The layer behaviour in the solutions of the examples is depicted in graphs.

show abstract

Mixed finite difference method for singularly perturbed differential difference equations with mixed shifts via domain decomposition

Cited by 16 publications

References 13 publications

Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

Computational Approach for a Singularly Perturbed Differential Equations With Mixed Shifts Using a Non-Polynomial Spline

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

Difference Scheme for Differential-Difference Problems with Small Shifts Arising in Computational Model of Neuronal Variability

Contact Info

Product

Resources

About