Numerical solutions of boundary value problems via fixed point iteration

被引：0

作者：

Saif, Mohammad ^{[1
]}

Almarri, Barakah ^{[2
]}

Aljuaid, Munirah ^{[3
]}

Uddin, Izhar ^{[1
,4
]}

机构：

[1] Jamia Millia Islamia, Dept Math, New Delhi 110025, India

[2] Jubail Ind Coll, Dept Gen Studies, 8244,Rd 6, Al Jubail 35718, Saudi Arabia

[3] Northern Border Univ, Coll Sci, Dept Math, Ar Ar, Saudi Arabia

[4] Near East Univ, Math Res Ctr, Dept Math, Near East Blvd,RNC Mersin 10, TR-99138 Nicosia, Turkiye

来源：

COMPUTATIONAL & APPLIED MATHEMATICS | 2024年 / 43卷 / 08期

关键词：

Fixed point; Weak contraction mapping; Green's function; Banach space; Convergence result; Second order boundary value problems; SCHEME; APPROXIMATION; THEOREM;

D O I：

10.1007/s40314-024-02933-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The aim of this paper is to solve second order nonlinear boundary value problems (BVPs) approximately. To do so, we utilize Thakur et al. iterative scheme (Filomat 3(10):2711-2720, 2016) involving a weak contraction mapping in an arbitrary Banach space. Firstly, we study the convergence behaviour and the two numerical examples to show the better rate of convergence. Further, we apply this method to find the approximate solution of nonlinear boundary value problems (BVPs) and two illustrative numerical examples for BVPs are provided. Thus, several corresponding results in the literature are generalised and improved.

引用

页数：22

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