On a monotone iterative method for a class of three point nonlinear nonsingular BVPs with upper and lower solutions in reverse order

2013 ◽  
Vol 43 (1-2) ◽  
pp. 99-114 ◽  
Author(s):  
Mandeep Singh ◽  
Amit K. Verma
Keyword(s):  
Iterative Method ◽  
Upper And Lower Solutions ◽  
Reverse Order ◽  
Monotone Iterative Method ◽  
Monotone Iterative

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 Picard Type Iterative Scheme with Initial Iterates in Reverse Order for a Class of Nonlinear Three Point BVPs

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Mandeep Singh ◽  
Amit K. Verma
Keyword(s):  
Source Term ◽  
Iterative Scheme ◽  
Upper And Lower Solutions ◽  
Sufficient Conditions ◽  
Existence Results ◽  
Monotone Iterative Technique ◽  
Reverse Order ◽  
Monotone Iterative Method ◽  
Iterative Technique ◽  
Monotone Iterative

We consider the following class of three point boundary value problemy′′(t)+f(t,y)=0,0<t<1,y′(0)=0,y(1)=δy(η), whereδ>0,0<η<1, the source termf(t,y)is Lipschitz and continuous. We use monotone iterative technique in the presence of upper and lower solutions for both well-order and reverse order cases. Under some sufficient conditions, we prove some new existence results. We use examples and figures to demonstrate that monotone iterative method can efficiently be used for computation of solutions of nonlinear BVPs.

Method of upper and lower solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments

2017 ◽  
Vol 67 (1) ◽  
pp. 89-98
Author(s):  
Neda Khodabakhshi ◽  
S. Mansour Vaezpour ◽  
J. Juan Trujillo
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Upper And Lower Solutions ◽  
Coupled System ◽  
Extremal Solutions ◽  
Monotone Iterative Method ◽  
Monotone Iterative

AbstractIn this paper, by means of upper and lower solutions, we develop monotone iterative method for the existence of extremal solutions for coupled system of nonlinear fractional integro-differential equations with advanced arguments. We illustrate this technique with the help of an example.

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