A fixed point iterative scheme based on Green's function for numerical solutions of singular BVPs

被引:4
作者
Ahmad, Junaid [1 ]
Arshad, Muhammad [1 ]
George, Reny [2 ]
机构
[1] Int Islamic Univ, Dept Math & Stat, H-10, Islamabad 44000, Pakistan
[2] Prince Sattam Bin Abdulaziz Univ, Coll Sci & Humanities Al Kharj, Dept Math, Al Kharj 11942, Saudi Arabia
来源
AIMS MATHEMATICS | 2023年 / 8卷 / 12期
关键词
solution; iteration scheme; boundary value problem; Green's function; Banach space; STABILITY; MAPPINGS; THEOREM; MANN; WEAK;
D O I
10.3934/math.20231511
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
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 w2-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.
引用
收藏
页码:29517 / 29534
页数:18
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