scholarly journals Exponentially convergent symbolic algorithm of the functional-discrete method for the fourth order Sturm–Liouville problems with polynomial coefficients

2019 ◽  
Vol 358 ◽  
pp. 405-423 ◽  
Author(s):  
Volodymyr L. Makarov ◽  
Nataliia M. Romaniuk
Keyword(s):  
Fourth Order ◽  
Discrete Method ◽  
Polynomial Coefficients ◽  
Sturm Liouville ◽  
Symbolic Algorithm

scholarly journals Symbolic Algorithm of the Functional-Discrete Method for a Sturm–Liouville Problem with a Polynomial Potential

2018 ◽  
Vol 18 (4) ◽  
pp. 703-715 ◽  
Author(s):  
Volodymyr Makarov ◽  
Nataliia Romaniuk
Keyword(s):  
Finite Interval ◽  
General Scheme ◽  
Liouville Problem ◽  
Piecewise Constant Function ◽  
Polynomial Potential ◽  
Discrete Method ◽  
Piecewise Constant ◽  
Sturm Liouville ◽  
Symbolic Algorithm ◽  
Theoretical Results

AbstractA new symbolic algorithmic implementation of the general scheme of the exponentially convergent functional-discrete method is developed and justified for the Sturm–Liouville problem on a finite interval for the Schrödinger equation with a polynomial potential and the boundary conditions of Dirichlet type. The algorithm of the general scheme of our method is developed when the potential function is approximated by the piecewise-constant function. Our algorithm is symbolic and operates with the decomposition coefficients of the eigenfunction corrections in some basis. The number of summands in these decompositions depends on the degree of the potential polynomial and on the correction number. Our method uses the algebraic operations only and does not need solutions of any boundary value problems and computations of any integrals unlike the previous version. A numerical example illustrates the theoretical results.

Functional-discrete Method (FD-method) for Matrix Sturm-Liouville Problems

2005 ◽  
Vol 5 (4) ◽  
pp. 362-386 ◽  
Author(s):  
B. Ĭ. Bandyrskiĭ ◽  
I. P. Gavrilyuk ◽  
I. I. Lazurchak ◽  
V. L. Makarov
Keyword(s):  
Asymptotic Behavior ◽  
Convergence Rate ◽  
Geometric Progression ◽  
Order Number ◽  
Discrete Method ◽  
Numerical Examples ◽  
Matrix Coefficients ◽  
Sturm Liouville ◽  
Theoretical Results

AbstractA new algorithm for Sturm|Liouville problems with matrix coefficients is proposed which possesses the convergence rate of a geometric progression with a denominator depending inversely proportional on the order number of eigenvalues. The asymptotic behavior of the distance between neighboring eigenvalues if the order number tends to infinity is investigated too. Numerical examples confirming the theoretical results are given.

scholarly journals ON THE SQUARE ROOT OF THE OPERATOR OF STURM-LIOUVILLE FOURTH-ORDER

2019 ◽  
Vol 3 (325) ◽  
pp. 85-96
Author(s):  
А.Sh. Shaldanbayev ◽  
◽  
A.B. Imanbayeva ◽  
A.Zh. Beisebayeva ◽  
А.А. Shaldanbayeva ◽  
...  
Keyword(s):  
Fourth Order ◽  
Square Root ◽  
Sturm Liouville
Sign in / Sign up

Export Citation Format

Share Document