Simple numerical methods of second- and third-order convergence for solving a fully third-order nonlinear boundary value problem

In this paper, we consider a fully third-order nonlinear boundary value problem that is of great interest of many researchers. First, we establish the existence and uniqueness of solution. Next, we propose simple iterative methods on both continuous and discrete levels. We prove that the discrete me...

Full description

Saved in:
Bibliographic Details
Published in:Numerical algorithms Vol. 87; no. 4; pp. 1479 - 1499
Main Authors: Dang, Quang A, Dang, Quang Long
Format: Journal Article
Language:English
Published: New York Springer US 01.08.2021
Springer Nature B.V
Subjects:
Accuracy
Algebra
Algorithms
Boundary conditions
Boundary value problems
Computer Science
Iterative methods
Methods
Numeric Computing
Numerical Analysis
Numerical integration
Numerical methods
Original Paper
Theory of Computation
Existence and uniqueness of solution
MSC 34B15
Iterative method
Total error
MSC 65L10
Third-order nonlinear equation
Third-order accuracy
ISSN:1017-1398, 1572-9265
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:In this paper, we consider a fully third-order nonlinear boundary value problem that is of great interest of many researchers. First, we establish the existence and uniqueness of solution. Next, we propose simple iterative methods on both continuous and discrete levels. We prove that the discrete methods are of second-order and third-order of accuracy due to the use of appropriate formulas for numerical integration and obtain estimate for total error. Some examples demonstrate the validity of the obtained theoretical results and the efficiency of the iterative methods.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:1017-1398
1572-9265
DOI:10.1007/s11075-020-01016-2