One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems
This paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods. The optimization process was integrated into the derivation of the methods to achieve maximal accuracy....
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2024-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2024/5078943 |
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| _version_ | 1832557240022728704 |
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| author | Saidu Daudu Yakubu Precious Sibanda |
| author_facet | Saidu Daudu Yakubu Precious Sibanda |
| author_sort | Saidu Daudu Yakubu |
| collection | DOAJ |
| description | This paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods. The optimization process was integrated into the derivation of the methods to achieve maximal accuracy. Through a rigorous analysis, it was determined that the methods exhibit properties of consistency, zero-stability, convergence, and A-stability. The proposed methods were implemented using the waveform relaxation technique, and the computed results demonstrated the superiority of these schemes over certain existing methods investigated in the study. |
| format | Article |
| id | doaj-art-6d9b6d0ddb174a179b901cbde154d467 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-6d9b6d0ddb174a179b901cbde154d4672025-02-03T05:32:36ZengWileyJournal of Applied Mathematics1687-00422024-01-01202410.1155/2024/5078943One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff ProblemsSaidu Daudu Yakubu0Precious Sibanda1School of MathematicsSchool of MathematicsThis paper introduces a novel approach for solving first-order stiff initial value problems through the development of a one-step family of three optimized second-derivative hybrid block methods. The optimization process was integrated into the derivation of the methods to achieve maximal accuracy. Through a rigorous analysis, it was determined that the methods exhibit properties of consistency, zero-stability, convergence, and A-stability. The proposed methods were implemented using the waveform relaxation technique, and the computed results demonstrated the superiority of these schemes over certain existing methods investigated in the study.http://dx.doi.org/10.1155/2024/5078943 |
| spellingShingle | Saidu Daudu Yakubu Precious Sibanda One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems Journal of Applied Mathematics |
| title | One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems |
| title_full | One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems |
| title_fullStr | One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems |
| title_full_unstemmed | One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems |
| title_short | One-Step Family of Three Optimized Second-Derivative Hybrid Block Methods for Solving First-Order Stiff Problems |
| title_sort | one step family of three optimized second derivative hybrid block methods for solving first order stiff problems |
| url | http://dx.doi.org/10.1155/2024/5078943 |
| work_keys_str_mv | AT saidudauduyakubu onestepfamilyofthreeoptimizedsecondderivativehybridblockmethodsforsolvingfirstorderstiffproblems AT precioussibanda onestepfamilyofthreeoptimizedsecondderivativehybridblockmethodsforsolvingfirstorderstiffproblems |