A two-sided iterative method for the solution of a boundary value problem for nonlinear systems of differential equations of parabolic and hyperbolic types

1969 ◽  
Vol 21 (2) ◽  
pp. 212-218
Author(s):  
Yu. I. Kovach ◽  
L. I. Savchenko
Keyword(s):  
Nonlinear Systems ◽  
Differential Equations ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Systems Of Differential Equations

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 method for solving the second boundary value problem (BVP) for Biharmonic type equation

2016 ◽  
Vol 14 (4) ◽  
pp. 66-72
Author(s):  
Đặng Quang Á
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Second Order ◽  
Second Order Equations

Solving BVPs for the fourth order differential equations by the reduction of them to BVPs for the  second order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by  ourselves in recent works, we construct iterative method for the second BVP for  biharmonic type equation. The convergence rate of  the method is established.

scholarly journals On the boundary value problem with integral conditions for the systems of differential equations of second order

1967 ◽  
Vol 7 (1) ◽  
pp. 59-77
Author(s):  
B. Kvedaras
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Boundary Value ◽  
Second Order ◽  
Integral Conditions ◽  
Systems Of Differential Equations

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Кведарас. О краевой задаче с интегральными условиями обыкновенных дифференциальных уравнений B. Kvedaras. Apie kraštinį uždavinį su integralinėmis sąlygomis antros eilės diferencialinių lygčių sistemoms

scholarly journals Iterative Method for Solving the Second Boundary Value Problem for Biharmonic-Type Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-18 ◽  
Author(s):  
Dang Quang A. ◽  
Nguyen Van Thien
Keyword(s):  
Differential Equations ◽  
Convergence Rate ◽  
Iterative Method ◽  
Boundary Value Problem ◽  
Fourth Order ◽  
Boundary Value ◽  
Type Equation ◽  
Numerical Examples ◽  
Optimal Value ◽  
Second Order Equations

Solving boundary value problems (BVPs) for the fourth-order differential equations by the reduction of them to BVPs for the second-order equations with the aim to use the achievements for the latter ones attracts attention from many researchers. In this paper, using the technique developed by ourselves in recent works, we construct iterative method for the second BVP for biharmonic-type equation, which describes the deflection of a plate resting on a biparametric elastic foundation. The convergence rate of the method is established. The optimal value of the iterative parameter is found. Several numerical examples confirm the efficiency of the proposed method.

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