Application of the averaging method for solving multipoint boundary-value problems with linear boundary condition for systems of volterra-type integrodifferential equations not solved for the derivative

1976 ◽  
Vol 28 (2) ◽  
pp. 192-196 ◽  
Author(s):  
S. D. Milusheva ◽  
D. D. Bainov
Keyword(s):  
Boundary Condition ◽  
Boundary Value Problems ◽  
Averaging Method ◽  
Boundary Value ◽  
Integrodifferential Equations ◽  
Linear Boundary ◽  
Volterra Type ◽  
Multipoint Boundary ◽  
Linear Boundary Condition ◽  
Multipoint Boundary Value Problems

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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