Higher-Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Differential Difference Equations with Mixed Small Shifts

Joint Authors

Woldaregay, Mesfin Mekuria
Duressa, Gemechis File

Source

International Journal of Differential Equations

Issue

Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-15, 15 p.

Publisher

Hindawi Publishing Corporation

Publication Date

2020-12-28

Country of Publication

Egypt

No. of Pages

15

Main Subjects

Mathematics

Abstract EN

This paper deals with numerical treatment of singularly perturbed differential difference equations involving mixed small shifts on the reaction terms.

The highest-order derivative term in the equation is multiplied by a small perturbation parameter ε taking arbitrary values in the interval 0,1.

For small values of ε, the solution of the problem exhibits exponential boundary layer on the left or right side of the domain and the derivatives of the solution behave boundlessly large.

The terms having the shifts are treated using Taylor’s series approximation.

The resulting singularly perturbed boundary value problem is solved using exponentially fitted operator FDM.

Uniform stability of the scheme is investigated and analysed using comparison principle and solution bound.

The formulated scheme converges uniformly with linear order before Richardson extrapolation and quadratic order after Richardson extrapolation.

The theoretical analysis of the scheme is validated using numerical test examples for different values of ε and mesh number N.

American Psychological Association (APA)

Woldaregay, Mesfin Mekuria& Duressa, Gemechis File. 2020. Higher-Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Differential Difference Equations with Mixed Small Shifts. International Journal of Differential Equations،Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1169961

Modern Language Association (MLA)

Woldaregay, Mesfin Mekuria& Duressa, Gemechis File. Higher-Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Differential Difference Equations with Mixed Small Shifts. International Journal of Differential Equations No. 2020 (2020), pp.1-15.
https://search.emarefa.net/detail/BIM-1169961

American Medical Association (AMA)

Woldaregay, Mesfin Mekuria& Duressa, Gemechis File. Higher-Order Uniformly Convergent Numerical Scheme for Singularly Perturbed Differential Difference Equations with Mixed Small Shifts. International Journal of Differential Equations. 2020. Vol. 2020, no. 2020, pp.1-15.
https://search.emarefa.net/detail/BIM-1169961

Data Type

Journal Articles

Language

English

Notes

Includes bibliographical references

Record ID

BIM-1169961