Numerical Solutions for Solving Special Tenth Order Linear Boundary Value Problems using Legendre Galerkin method

2018 ◽  
Vol 7 (1) ◽  
pp. 27-35 ◽  
Author(s):  
Zaffer Elahi ◽  
Ghazala Akram ◽  
Shahid S. Siddiqi
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Linear Boundary ◽  
Order Linear ◽  
Legendre Galerkin Method

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.

scholarly journals Modified Sinc-Galerkin Method for Nonlinear Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
M. A. Hajji ◽  
Q. M. Al-Mdallal
Keyword(s):  
Galerkin Method ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Numerical Solutions ◽  
Boundary Value ◽  
Basis Functions ◽  
Accurate Approximation ◽  
Nonlinear Boundary Value Problems ◽  
Thomas Fermi ◽  
Nonlinear Boundary Value

This paper presents a modified Galerkin method based on sinc basis functions to numerically solve nonlinear boundary value problems. The modifications allow for the accurate approximation of the solution with accurate derivatives at the endpoints. The algorithm is applied to well-known problems: Bratu and Thomas-Fermi problems. Numerical results demonstrate the clear advantage of the suggested modifications in obtaining accurate numerical solutions as well as accurate derivatives at the endpoints.

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