On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications
In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from...
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Journal of Function Spaces |
| Online Access: | http://dx.doi.org/10.1155/2019/4042965 |
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| _version_ | 1832563838974689280 |
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| author | Teng-fei Li Heng-you Lan |
| author_facet | Teng-fei Li Heng-you Lan |
| author_sort | Teng-fei Li |
| collection | DOAJ |
| description | In order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. Further, some numerical examples and applications to optimal control problems with elliptic boundary value constraints are considered via the new Picard-Mann iterative approximations, which shows that the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes. |
| format | Article |
| id | doaj-art-414eb508e7d1462793ede96e5d58c145 |
| institution | Kabale University |
| issn | 2314-8896 2314-8888 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces |
| spelling | doaj-art-414eb508e7d1462793ede96e5d58c1452025-02-03T01:12:26ZengWileyJournal of Function Spaces2314-88962314-88882019-01-01201910.1155/2019/40429654042965On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and ApplicationsTeng-fei Li0Heng-you Lan1Department of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan 430081, Hubei, ChinaCollege of Mathematics and Statistics, Sichuan University of Science & Engineering, Zigong, Sichuan 643000, ChinaIn order to solve (partial) differential equations, implicit midpoint rules are often employed as a powerful numerical method. The purpose of this paper is to introduce and study a class of new Picard-Mann iteration processes with mixed errors for the implicit midpoint rules, which is different from existing methods in the literature, and to analyze the convergence and stability of the proposed method. Further, some numerical examples and applications to optimal control problems with elliptic boundary value constraints are considered via the new Picard-Mann iterative approximations, which shows that the new Picard-Mann iteration process with mixed errors for the implicit midpoint rule of nonexpansive mappings is brand new and more effective than other related iterative processes.http://dx.doi.org/10.1155/2019/4042965 |
| spellingShingle | Teng-fei Li Heng-you Lan On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications Journal of Function Spaces |
| title | On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications |
| title_full | On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications |
| title_fullStr | On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications |
| title_full_unstemmed | On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications |
| title_short | On New Picard-Mann Iterative Approximations with Mixed Errors for Implicit Midpoint Rule and Applications |
| title_sort | on new picard mann iterative approximations with mixed errors for implicit midpoint rule and applications |
| url | http://dx.doi.org/10.1155/2019/4042965 |
| work_keys_str_mv | AT tengfeili onnewpicardmanniterativeapproximationswithmixederrorsforimplicitmidpointruleandapplications AT hengyoulan onnewpicardmanniterativeapproximationswithmixederrorsforimplicitmidpointruleandapplications |