Converging efficiency: Computational and fractal insights into parallel non-linear schemes
This study presents and examines a parallel method for the simultaneous approximation of all roots of nonlinear equations. With the use of a parallel computing architecture, the algorithm aims to enhance computational efficiency. An exhaustive convergence analysis corroborates the finding that the d...
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| Format: | Article |
| Language: | English |
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Elsevier
2025-11-01
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| Series: | Ain Shams Engineering Journal |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S2090447925004113 |
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| author | Mudassir Shams Nasreen Kausar Ali Akgül Tonguç Çağın |
| author_facet | Mudassir Shams Nasreen Kausar Ali Akgül Tonguç Çağın |
| author_sort | Mudassir Shams |
| collection | DOAJ |
| description | This study presents and examines a parallel method for the simultaneous approximation of all roots of nonlinear equations. With the use of a parallel computing architecture, the algorithm aims to enhance computational efficiency. An exhaustive convergence analysis corroborates the finding that the developed scheme converges at sixth order. To optimize parameter values and speed up the convergence rate of the proposed parallel technique, the concepts of dynamical and parametric planes are employed. The computational efficiency percentage demonstrates that the new parallel method is more efficient and involves fewer arithmetic operations compared to the current methods. Randomly chosen initial values are employed to demonstrate the engineering problems have been subjected to comparative analysis, which shows that the suggested parallel schemes surpass traditional methods in residual error, convergence rate, CPU time, memory usage, and computational cost. The findings indicate that the approach holds promise as a means of addressing nonlinear equations in scientific and engineering contexts. |
| format | Article |
| id | doaj-art-e0ae06e6b30543299ff85d9f4a5488b9 |
| institution | Kabale University |
| issn | 2090-4479 |
| language | English |
| publishDate | 2025-11-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Ain Shams Engineering Journal |
| spelling | doaj-art-e0ae06e6b30543299ff85d9f4a5488b92025-08-20T03:44:14ZengElsevierAin Shams Engineering Journal2090-44792025-11-01161110367010.1016/j.asej.2025.103670Converging efficiency: Computational and fractal insights into parallel non-linear schemesMudassir Shams0Nasreen Kausar1Ali Akgül2Tonguç Çağın3Department of Mathematics, Faculty of Arts and Science, Balikesir University, Balikesir 10145, TurkeyDepartment of Mathematics, Faculty of Arts and Science, Balikesir University, Balikesir 10145, TurkeyDepartment of Electronics and Communication Engineering, Saveetha School of Engineering, SIMATS, Chennai, Tamilnadu, India; Siirt University, Art and Science Faculty, Department of Mathematics, 56100 Siirt, Turkey; Department of Computer Engineering, Biruni University, 34010 Topkapı, Istanbul, Turkey; Near East University, Mathematics Research Center, Department of Mathematics, Near East Boulevard, PC: 99138, Nicosia, Mersin 10, Turkey; Applied Science Research Center, Applied Science Private University, Amman, JordanCollege of Business Administration, American University of the Middle East, Kuwait; Corresponding author.This study presents and examines a parallel method for the simultaneous approximation of all roots of nonlinear equations. With the use of a parallel computing architecture, the algorithm aims to enhance computational efficiency. An exhaustive convergence analysis corroborates the finding that the developed scheme converges at sixth order. To optimize parameter values and speed up the convergence rate of the proposed parallel technique, the concepts of dynamical and parametric planes are employed. The computational efficiency percentage demonstrates that the new parallel method is more efficient and involves fewer arithmetic operations compared to the current methods. Randomly chosen initial values are employed to demonstrate the engineering problems have been subjected to comparative analysis, which shows that the suggested parallel schemes surpass traditional methods in residual error, convergence rate, CPU time, memory usage, and computational cost. The findings indicate that the approach holds promise as a means of addressing nonlinear equations in scientific and engineering contexts.http://www.sciencedirect.com/science/article/pii/S2090447925004113Parallel schemeEngineering problemsComplex dynamicsFractalResidual error |
| spellingShingle | Mudassir Shams Nasreen Kausar Ali Akgül Tonguç Çağın Converging efficiency: Computational and fractal insights into parallel non-linear schemes Ain Shams Engineering Journal Parallel scheme Engineering problems Complex dynamics Fractal Residual error |
| title | Converging efficiency: Computational and fractal insights into parallel non-linear schemes |
| title_full | Converging efficiency: Computational and fractal insights into parallel non-linear schemes |
| title_fullStr | Converging efficiency: Computational and fractal insights into parallel non-linear schemes |
| title_full_unstemmed | Converging efficiency: Computational and fractal insights into parallel non-linear schemes |
| title_short | Converging efficiency: Computational and fractal insights into parallel non-linear schemes |
| title_sort | converging efficiency computational and fractal insights into parallel non linear schemes |
| topic | Parallel scheme Engineering problems Complex dynamics Fractal Residual error |
| url | http://www.sciencedirect.com/science/article/pii/S2090447925004113 |
| work_keys_str_mv | AT mudassirshams convergingefficiencycomputationalandfractalinsightsintoparallelnonlinearschemes AT nasreenkausar convergingefficiencycomputationalandfractalinsightsintoparallelnonlinearschemes AT aliakgul convergingefficiencycomputationalandfractalinsightsintoparallelnonlinearschemes AT tonguccagın convergingefficiencycomputationalandfractalinsightsintoparallelnonlinearschemes |