scholarly journals A Barycentric Interpolation Collocation Method for Linear Nonlocal Boundary Value Problems

2016 ◽  
Vol 10 (11) ◽  
pp. 140
Author(s):  
Dan Tian ◽  
Weiya Li ◽  
Cec Yulan Wang
Keyword(s):  
Boundary Value Problem ◽  
Collocation Method ◽  
Present Method ◽  
Lagrange Interpolation ◽  
Boundary Value ◽  
Nonlocal Boundary ◽  
Higher Order ◽  
Point Boundary ◽  
Numerical Treatment ◽  
Barycentric Interpolation

This paper is devoted to the numerical treatment of a class of higher-order multi-point boundary value problem-s(BVPs). The method is proposed based on the Lagrange interpolation collocation method, but it avoids thenumerical instability of Lagrange interpolation. Numerical results obtained by present method compare with othermethods show that the present method is simple and accurate for higher-order multi-point BVPs, and it is eectivefor solving six order or higher order multi-point BVPs.

scholarly journals Solutions of a multi-point boundary value problem for higher-order differential equations at resonance (III)

2005 ◽  
Vol 36 (2) ◽  
pp. 119-130 ◽  
Author(s):  
Yuji Liu ◽  
Weigao Ge
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Point Boundary ◽  
At Resonance ◽  
Higher Order Differential Equations

In this paper, we are concerned with the existence of solutions of the following multi-point boundary value problem consisting of the higher-order differential equations$ x^{(n)}(t)=f(t,x(t),x'(t),\cdots,x^{(n-1)}(t))+e(t),\;\;0

scholarly journals Existence and Nonexistence of Positive Solutions for a Higher-Order Three-Point Boundary Value Problem

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Yongping Sun ◽  
Qian Sun ◽  
Xiaoping Zhang
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
Existence Results ◽  
Functional Type ◽  
Point Boundary ◽  
Existence And Nonexistence ◽  
Cone Expansion And Compression

This paper is concerned with the existence and nonexistence of positive solutions for a nonlinear higher-order three-point boundary value problem. The existence results are obtained by applying a fixed point theorem of cone expansion and compression of functional type due to Avery, Henderson, and O’Regan.

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