A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs
We suggest a novel iterative scheme for solutions of singular boundary value problems (SBVPs) that is obtained by embedding Green's function into the Picard-Mann Hybrid (PMH) iterative scheme. This new scheme we call PMH-Green's iterative scheme and prove its convergence towards a sought s...
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-10-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231511?viewType=HTML |
| _version_ | 1827699853454475264 |
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| author | Junaid Ahmad Muhammad Arshad Reny George |
| author_facet | Junaid Ahmad Muhammad Arshad Reny George |
| author_sort | Junaid Ahmad |
| collection | DOAJ |
| description | We suggest a novel iterative scheme for solutions of singular boundary value problems (SBVPs) that is obtained by embedding Green's function into the Picard-Mann Hybrid (PMH) iterative scheme. This new scheme we call PMH-Green's iterative scheme and prove its convergence towards a sought solution of certain SBVPs. We impose possible mild conditions on the operator or on the parameters involved in our scheme to obtain our main outcome. After this, we prove that this new iterative scheme is weak $ w^{2} $-stable. Eventually, using two different numerical examples of SBVPs, we show that our new approach suggests highly accurate numerical solutions as compared the corresponding Picard-Green's and Mann-Green's iterative schemes. |
| first_indexed | 2024-03-10T14:00:20Z |
| format | Article |
| id | doaj.art-af66e83a7f824f4bb2b6f2dd59ef1d59 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-10T14:00:20Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-af66e83a7f824f4bb2b6f2dd59ef1d592023-11-21T01:15:43ZengAIMS PressAIMS Mathematics2473-69882023-10-01812295172953410.3934/math.20231511A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPsJunaid Ahmad0Muhammad Arshad1Reny George21. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan1. Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad-44000, Pakistan2. Department of Mathematics, College of Science and Humanities in Al-Kharj, Prince Sattam Bin Abdulaziz University, Al-Kharj 11942, Saudi ArabiaWe suggest a novel iterative scheme for solutions of singular boundary value problems (SBVPs) that is obtained by embedding Green's function into the Picard-Mann Hybrid (PMH) iterative scheme. This new scheme we call PMH-Green's iterative scheme and prove its convergence towards a sought solution of certain SBVPs. We impose possible mild conditions on the operator or on the parameters involved in our scheme to obtain our main outcome. After this, we prove that this new iterative scheme is weak $ w^{2} $-stable. Eventually, using two different numerical examples of SBVPs, we show that our new approach suggests highly accurate numerical solutions as compared the corresponding Picard-Green's and Mann-Green's iterative schemes.https://www.aimspress.com/article/doi/10.3934/math.20231511?viewType=HTMLsolutioniteration schemeboundary value problemgreen's functionbanach space |
| spellingShingle | Junaid Ahmad Muhammad Arshad Reny George A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs AIMS Mathematics solution iteration scheme boundary value problem green's function banach space |
| title | A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs |
| title_full | A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs |
| title_fullStr | A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs |
| title_full_unstemmed | A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs |
| title_short | A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs |
| title_sort | fixed point iterative scheme based on green s function for numerical solutions of singular bvps |
| topic | solution iteration scheme boundary value problem green's function banach space |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231511?viewType=HTML |
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