An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations
The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical sim...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2022-01-01
|
| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2022/8961352 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1849396687024422912 |
|---|---|
| author | Fathalla A. Rihan Ahmed F. Rihan |
| author_facet | Fathalla A. Rihan Ahmed F. Rihan |
| author_sort | Fathalla A. Rihan |
| collection | DOAJ |
| description | The pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ-methods, with ϑ>1/2, are effective in resolving stiff pantograph problems. |
| format | Article |
| id | doaj-art-affb2df06c8643c3ae765074cb2d6769 |
| institution | Kabale University |
| issn | 1099-0526 |
| language | English |
| publishDate | 2022-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-affb2df06c8643c3ae765074cb2d67692025-08-20T03:39:15ZengWileyComplexity1099-05262022-01-01202210.1155/2022/8961352An Analysis of the Theta-Method for Pantograph-Type Delay Differential EquationsFathalla A. Rihan0Ahmed F. Rihan1Department of Mathematical SciencesDepartment of Electrical EngineeringThe pantograph equation arises in electrodynamics as a delay differential equation (DDE). In this article, we provide the ϑ-method for numerical solutions of pantograph equations. We investigate the stability conditions for the numerical schemes. The theoretical results are verified by numerical simulations. The theoretical results and numerical simulations show that implicit or partially implicit ϑ-methods, with ϑ>1/2, are effective in resolving stiff pantograph problems.http://dx.doi.org/10.1155/2022/8961352 |
| spellingShingle | Fathalla A. Rihan Ahmed F. Rihan An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations Complexity |
| title | An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations |
| title_full | An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations |
| title_fullStr | An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations |
| title_full_unstemmed | An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations |
| title_short | An Analysis of the Theta-Method for Pantograph-Type Delay Differential Equations |
| title_sort | analysis of the theta method for pantograph type delay differential equations |
| url | http://dx.doi.org/10.1155/2022/8961352 |
| work_keys_str_mv | AT fathallaarihan ananalysisofthethetamethodforpantographtypedelaydifferentialequations AT ahmedfrihan ananalysisofthethetamethodforpantographtypedelaydifferentialequations AT fathallaarihan analysisofthethetamethodforpantographtypedelaydifferentialequations AT ahmedfrihan analysisofthethetamethodforpantographtypedelaydifferentialequations |