A new fixed point algorithm for finding the solution of a delay differential equation
In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for appr...
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| Vydané v: | AIMS mathematics Ročník 5; číslo 4; s. 3182 - 3200 |
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| Médium: | Journal Article |
| Jazyk: | English |
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AIMS Press
01.01.2020
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| ISSN: | 2473-6988, 2473-6988 |
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| Abstract | In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating fixed points of Suzuki generalized nonexpansive mappings. Again we reconfirm our results by example and table. Further, we utilize our proposed algorithm to solve delay differential equation. |
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| AbstractList | In this paper, we construct a new iterative algorithm and show that the newly introduced iterative algorithm converges faster than a number of existing iterative algorithms. We present a numerical example followed by graphs to validate our claim. We prove strong and weak convergence results for approximating fixed points of Suzuki generalized nonexpansive mappings. Again we reconfirm our results by example and table. Further, we utilize our proposed algorithm to solve delay differential equation. |
| Author | Garodia, Chanchal Uddin, Izhar |
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| Cites_doi | 10.1016/j.jmaa.2018.06.025 10.1006/jmaa.1993.1309 10.2298/FIL1801187U 10.1016/j.nahs.2010.12.006 10.1016/j.jmaa.2010.08.069 10.1007/s00211-012-0467-7 10.1016/j.nahs.2017.07.002 10.1016/j.jmaa.2007.09.023 10.1017/S0004972700028884 10.1090/S0002-9904-1967-11864-0 10.1016/j.jmaa.2008.08.045 10.1007/BF01304884 10.1007/s11464-009-0008-6 10.1016/j.cam.2010.12.022 10.1090/S0002-9939-1953-0054846-3 10.2298/FIL1610711T 10.1090/S0002-9939-1974-0336469-5 10.1016/j.cam.2019.04.001 10.1090/S0002-9939-1974-0346608-8 10.1016/j.na.2011.05.078 10.1006/jmaa.2000.7042 |
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| References | M. A. Noor (20) 28 L. Xu, S. Sam Ge (33) B. Halpern (12) C. Huang, S. Vandewalle (14) W. R. Mann (19) T. Suzuki (26) 30 T. Zamfirescu (34) W. Phuengrattana, S. Suantai (21) L. Xu, Z. Dai, H. Hu (32) 35 16 S. Dhompongsa, W. Inthakon, A. Kaewkhao (9) J. Schu (24) 1 D. R. Sahu, A. Petrusel (23) 2 C. Huang, S. Vandewalle (15) 3 J. Garcia-Falset, E. Llorens-Fuster, T. Suzuki (10) H. F. Senter, W. G. Dotson (25) 4 H. Hu, L. Xu (13) 5 6 K. K. Tan, H. K. Xu (27) 7 K. Ullah, M. Arshad (31) S. Ishikawa (17) W. Phuengrattana (22) D. Thakur, B. S. Thakur, M. Postolache (29) |
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| SubjectTerms | contractive-like mappings delay differential equation fixed point iteration process strong and weak convergence suzuki generalized nonexpansive mappings |
| Title | A new fixed point algorithm for finding the solution of a delay differential equation |
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