Interval length continuation method for solving two-point boundary-value problems

1977 ◽  
Vol 23 (2) ◽  
pp. 217-227 ◽  
Author(s):  
P. J. Orava ◽  
P. A. J. Lautala
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Continuation Method ◽  
Interval Length ◽  
Point Boundary

Interval length imbedding for nonlinear two-point boundary-value problems

1974 ◽  
Vol 13 (2) ◽  
pp. 159-163 ◽  
Author(s):  
J. Casti ◽  
R. Kalaba ◽  
G. Meier ◽  
E. Zagustin
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Interval Length ◽  
Point Boundary

scholarly journals The Solutions of Second Order Nonlinear Two Point Boundary Value Problems

2019 ◽  
Vol 4 (8) ◽  
pp. 49-54
Author(s):  
Abdurkadir Edeo Gemeda
Keyword(s):  
Nonlinear Systems ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Continuation Method ◽  
Operational Matrix ◽  
Approximate Solutions ◽  
Second Order ◽  
Point Boundary ◽  
Algebraic Equations ◽  
Operational Matrix Of Differentiation

In this paper, generalized shifted Legendre polynomial approximation on a given arbitrary interval has been designed to find an approximate solution of a given second order nonlinear two point boundary value problems of ordinary differential equations. Here an approach using Tau method based on Legendre operational matrix of differentiation [2] & [5] has been addressed to generate the nonlinear systems of algebraic equations. The unknown Legendre coefficients of these nonlinear systems are the solutions of the system and they have been solved by continuation method. These unknown Legendre coefficients are then used to write the approximate solutions to the second order nonlinear two point boundary value problems. The validity and efficiency of the method has also been illustrated with numerical examples and graphs assisted by MATLAB.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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