Precision in Second-order FBVP Solutions Using a Combined Ishikawa–Green’s Approach

In this study, we introduce a novel numerical technique designed to solve a wide range of second-order fractional boundary value problems (FBVPs). The proposed method incorporates an integral operator, expressed in terms of Green’s function, within the framework of the Ishikawa fixed point iteration...

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Bibliographic Details
Published inLobachevskii journal of mathematics Vol. 45; no. 12; pp. 6111 - 6120
Main Author Khuri, S. A.
Format Journal Article
LanguageEnglish
Published Moscow Pleiades Publishing 01.12.2024
Springer Nature B.V
Subjects
Algebra
Analysis
Boundary value problems
Geometry
Green's functions
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operators (mathematics)
Probability Theory and Stochastic Processes
2010 Mathematics Subject Classification: 34A08, 34B15, 47H10, 65L10
Green’s function
Ishikawa fixed point scheme
fractional boundary value problems
contraction mapping
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Summary:In this study, we introduce a novel numerical technique designed to solve a wide range of second-order fractional boundary value problems (FBVPs). The proposed method incorporates an integral operator, expressed in terms of Green’s function, within the framework of the Ishikawa fixed point iteration scheme. The effectiveness and robustness of the technique are validated through various examples. Detailed analyses of residual errors indicate that this method provides highly accurate approximations, demonstrating its potential for effectively addressing second-order FBVPs.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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ISSN:1995-0802
1818-9962
DOI:10.1134/S199508022460746X