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

共 50 条

[31] NONNEGATIVE SOLUTIONS IN TWO POINT BOUNDARY VALUE PROBLEMS
Matehkolaee, Mahmood Jaafari
JOURNAL OF SCIENCE AND ARTS, 2012, (01): : 39 - 42
[32] Solution of the Boundary Value Problems via Fixed Point Theorem on G-metric Space
Thirumalai, R. Anna
Thalapathiraj, S.
IAENG International Journal of Applied Mathematics, 2023, 53 (04)
[33] Existence of solutions for a class of fractional boundary value problems via critical point theory
Jiao, Feng
Zhou, Yong
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2011, 62 (03) : 1181 - 1199
[34] Variational iteration method for solving two-point boundary value problems
Lu, Junfeng
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2007, 207 (01) : 92 - 95
[35] Fourth-Order Solutions of Nonlinear Two-Point Boundary Value Problems By Newton-HSSOR Iteration
Sulaiman, Jumat
Hasan, Mohd Khatim
Othman, Mohamed
Karim, Samsul Ariffin Abdul
PROCEEDINGS OF THE 3RD INTERNATIONAL CONFERENCE ON MATHEMATICAL SCIENCES, 2014, 1602 : 69 - 75
[36] Solutions of two-point boundary value problems via phase-plane analysis
Atslega, Svetlana
Sadyrbaev, Felix
ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2016,
[37] PARALLEL COMPUTATION OF 2-POINT BOUNDARY-VALUE-PROBLEMS VIA PARTICULAR SOLUTIONS
MIELE, A
WANG, T
JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS, 1993, 79 (01) : 5 - 29
[38] Fixed-point approach for nonlinear discrete boundary value problems
Agarwal, R.P.
O'Regan, D.
Computers and Mathematics with Applications, 1998, 36 (10-12): : 115 - 121
[39] A fixed-point approach for nonlinear discrete boundary value problems
Agarwal, RP
O'Regan, D
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1998, 36 (10-12) : 115 - 121
[40] COUPLED FIXED POINT THEOREMS AND APPLICATIONS TO PERIODIC BOUNDARY VALUE PROBLEMS
Urs, Cristina
MISKOLC MATHEMATICAL NOTES, 2013, 14 (01) : 323 - 333

← 1 2 3 4 5 →