Monotone iterative method for the second-order three-point boundary value problem with upper and lower solutions in the reversed order

2011 ◽  
Vol 217 (9) ◽  
pp. 4840-4847 ◽  
Author(s):  
Fangfei Li ◽  
Jitao Sun ◽  
Mei Jia
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Second Order ◽  
Monotone Iterative Method ◽  
Point Boundary ◽  
Monotone Iterative ◽  
Reversed Order

scholarly journals A monotone iterative method for boundary value problems of parametric differential equations

2001 ◽  
Vol 14 (2) ◽  
pp. 183-187 ◽  
Author(s):  
Xinzhi Liu ◽  
Farzana A. McRae
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Monotone Sequences

This paper studies boundary value problems for parametric differential equations. By using the method of upper and lower solutions, monotone sequences are constructed and proved to converge to the extremal solutions of the boundary value problem.

scholarly journals Iterative Approximation of the Minimal and Maximal Positive Solutions for Multipoint Fractional Boundary Value Problem on an Unbounded Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Guotao Wang ◽  
Sanyang Liu ◽  
Lihong Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Unbounded Domain ◽  
Boundary Value ◽  
Monotone Iterative Method ◽  
Fractional Boundary Value Problem ◽  
Iterative Approximation ◽  
Monotone Iterative

By employing the monotone iterative method, this paper not only establishes the existence of the minimal and maximal positive solutions for multipoint fractional boundary value problem on an unbounded domain, but also develops two computable explicit monotone iterative sequences for approximating the two positive solutions. An example is given for the illustration of the main result.

scholarly journals Monotone methods for solving a boundary value problem of second order discrete system

1999 ◽  
Vol 5 (4) ◽  
pp. 291-315 ◽  
Author(s):  
Yuan-Ming Wang ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Discrete System ◽  
Iterative Scheme ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Second Order ◽  
Monotone Convergence ◽  
Monotone Iterative ◽  
System A ◽  
Monotone Methods

A new concept of a pair of upper and lower solutions is introduced for a boundary value problem of second order discrete system. A comparison result is given. An existence theorem for a solution is established in terms of upper and lower solutions. A monotone iterative scheme is proposed, and the monotone convergence rate of the iteration is compared and analyzed. The numerical results are given.

scholarly journals Fixed point theorems via Generalized WF-Contractions with applications

SeMA Journal ◽  
2021 ◽  
Author(s):  
Rosana Rodríguez-López ◽  
Rakesh Tiwari
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Fixed Point Theorems ◽  
Boundary Value ◽  
Second Order ◽  
Point Boundary ◽  
New Class ◽  
Second Order Differential Equations ◽  
Fixed Point Result

AbstractThe aim of this paper is to introduce a new class of mixed contractions which allow to revise and generalize some results obtained in [6] by R. Gubran, W. M. Alfaqih and M. Imdad. We also provide an example corresponding to this class of mappings and show how the new fixed point result relates to the above-mentioned result in [6]. Further, we present an application to the solvability of a two-point boundary value problem for second order differential equations.

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