Spline Approximate Solutions of Arbitrary Order Linear Boundary Value Problems

2011 ◽  
Author(s):  
Xinze Lian ◽  
Chengsheng Lin ◽  
Guichen Lu
Keyword(s):  
Boundary Value Problems ◽  
Arbitrary Order ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Linear Boundary ◽  
Order Linear

scholarly journals Solvability ofNth Order Linear Boundary Value Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-19 ◽  
Author(s):  
P. Almenar ◽  
L. Jódar
Keyword(s):  
Integral Operator ◽  
Boundary Value Problems ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Linear Boundary ◽  
Order Linear ◽  
Linear Integral ◽  
Necessary And Sufficient

This paper presents a method that provides necessary and sufficient conditions for the existence of solutions ofnth order linear boundary value problems. The method is based on the recursive application of a linear integral operator to some functions and the comparison of the result with these same functions. The recursive comparison yields sequences of bounds of extremes that converge to the exact values of the extremes of the BVP for which a solution exists.

scholarly journals The principal eigenvalue of some nth order linear boundary value problems

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Pedro Almenar ◽  
Lucas Jódar
Keyword(s):  
Integral Operator ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Principal Eigenvalue ◽  
Green Functions ◽  
Linear Boundary ◽  
Order Linear

AbstractThe purpose of this paper is to present a procedure for the estimation of the smallest eigenvalues and their associated eigenfunctions of nth order linear boundary value problems with homogeneous boundary conditions defined in terms of quasi-derivatives. The procedure is based on the iterative application of the equivalent integral operator to functions of a cone and the calculation of the Collatz–Wielandt numbers of such functions. Some results on the sign of the Green functions of the boundary value problems are also provided.

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