Application of the averaging method for solving multipoint boundary-value problems with nonlinear boundary condition for systems of differential and integrodifferential equations not solved with respect to the derivative

1977 ◽  
Vol 29 (2) ◽  
pp. 199-203 ◽  
Author(s):  
S. D. Milusheva ◽  
D. D. Vainov
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Nonlinear Boundary Condition ◽  
Averaging Method ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems

scholarly journals Nonlinear multipoint boundary value problems for weakly coupled systems

1999 ◽  
Vol 60 (1) ◽  
pp. 45-54 ◽  
Author(s):  
H.B. Thompson ◽  
C.C. Tisdell
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Existence Results ◽  
Coupled Systems ◽  
Multipoint Boundary ◽  
Weakly Coupled ◽  
Weakly Coupled Systems ◽  
Multipoint Boundary Value Problems

We establish existence results concerning solutions to multipoint boundary value problems for weakly coupled systems of second order ordinary differential equations with fully nonlinear boundary conditions.

scholarly journals Numerov's Method for a Class of Nonlinear Multipoint Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-29
Author(s):  
Yuan-Ming Wang ◽  
Wen-Jia Wu ◽  
Massimo Scalia
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Fourth Order ◽  
High Efficiency ◽  
Boundary Value ◽  
Upper And Lower Solutions ◽  
Multipoint Boundary ◽  
Discrete Problems ◽  
Multipoint Boundary Value Problems ◽  
Multipoint Boundary Condition

The purpose of this paper is to give a numerical treatment for a class of nonlinear multipoint boundary value problems. The multipoint boundary condition under consideration includes various commonly discussed boundary conditions, such as the three- or four-point boundary condition. The problems are discretized by the fourth-order Numerov's method. The existence and uniqueness of the numerical solution are investigated by the method of upper and lower solutions. The convergence and the fourth-order accuracy of the method are proved. An accelerated monotone iterative algorithm with the quadratic rate of convergence is developed for solving the resulting nonlinear discrete problems. Some applications and numerical results are given to demonstrate the high efficiency of the approach.

Multipoint Boundary Value Problems

Equadiff 99 ◽  
2000 ◽  
pp. 485-487
Author(s):  
Abdelkader Boucherif ◽  
Sidi Mohamed Bouguima
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Multipoint Boundary ◽  
Multipoint Boundary Value Problems
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