Monotone-iterative method for a mixed nonlinear boundary value problem for differential equations with "maxima"

2012 ◽  
Author(s):  
S. Hristova ◽  
K. Stefanova
Keyword(s):  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Nonlinear Boundary Value

scholarly journals Monotone-Iterative Method for Solving Antiperiodic Nonlinear Boundary Value Problems for Generalized Delay Difference Equations with Maxima

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Angel Golev ◽  
Snezhana Hristova ◽  
Svetoslav Nenov
Keyword(s):  
Difference Equation ◽  
Boundary Value Problem ◽  
Unknown Function ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Monotone Iterative Method ◽  
Monotone Iterative ◽  
Nonlinear Boundary Value ◽  
The Given

A nonlinear generalized difference equation with both delays and the maximum value of the unknown function over a discrete past time interval are studied. A nonlinear boundary value problem of antiperiodic type for the given difference equation is set up. One of the main characteristics of the considered difference equation is the presence of the unknown function in both sides of the equation. It leads to impossibility for using the step method for explicit solving of the nonlinear difference equation. In this paper, an approximate method, namely, the monotone iterative technique, is applied to solve the problem. An important feature of the given algorithm is that each successive approximation of the unknown solution is equal to the unique solution of an appropriately constructed initial value problem for a linear difference equation with “maxima,” and an algorithm for its explicit solving is given. Also, each approximation is a lower/upper solution of the given nonlinear boundary value problem. The suggested scheme for approximate solving is computer realized, and it is applied to a particular example, which is a generalization of a model in population dynamics.

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 Pointwise bounds for a solution of a nonlinear boundary value problem in partial differential equations

1983 ◽  
Vol 24 (4) ◽  
pp. 366-373
Author(s):  
N. Anderson ◽  
A. M. Arthurs
Keyword(s):  
Dirichlet Problem ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Boundary Value Problem ◽  
Liouville Equation ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Value Problem ◽  
Partial Differential ◽  
Nonlinear Boundary Value

AbstractPointwise bounds are obtained for the solution of a Dirichlet problem involving the nonlinear Liouville equation in the plane, Illustrative calculations are performed for a square domain.

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