TY - JOUR
T1 - Computing eigenpairs of two-parameter Sturm-Liouville systems using the bivariate sinc-Gauss formula
AU - Asharabi, Rashad M.
AU - Prestin, Jürgen
N1 - Publisher Copyright:
© 2020 American Institute of Mathematical Sciences. All rights reserved.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.
PY - 2020/8
Y1 - 2020/8
N2 - The use of sampling methods in computing eigenpairs of twoparameter boundary value problems is extremely rare. As far as we know, there are only two studies up to now using the bivariate version of the classical and regularized sampling series. These series have a slow convergence rate. In this paper, we use the bivariate sinc-Gauss sampling formula that was proposed in [6] to construct a new sampling method to compute eigenpairs of a two-parameter Sturm-Liouville system. The convergence rate of this method will be of exponential order, i.e. O(e-δN/√N) where δ is a positive number and N is the number of terms in the bivariate sinc-Gaussian formula. We estimate the amplitude error associated to this formula, which gives us the possibility to establish the rigorous error analysis of this method. Numerical illustrative examples are presented to demonstrate our method in comparison with the results of the bivariate classical sampling method.
AB - The use of sampling methods in computing eigenpairs of twoparameter boundary value problems is extremely rare. As far as we know, there are only two studies up to now using the bivariate version of the classical and regularized sampling series. These series have a slow convergence rate. In this paper, we use the bivariate sinc-Gauss sampling formula that was proposed in [6] to construct a new sampling method to compute eigenpairs of a two-parameter Sturm-Liouville system. The convergence rate of this method will be of exponential order, i.e. O(e-δN/√N) where δ is a positive number and N is the number of terms in the bivariate sinc-Gaussian formula. We estimate the amplitude error associated to this formula, which gives us the possibility to establish the rigorous error analysis of this method. Numerical illustrative examples are presented to demonstrate our method in comparison with the results of the bivariate classical sampling method.
UR - http://www.scopus.com/inward/record.url?scp=85090760541&partnerID=8YFLogxK
U2 - 10.3934/cpaa.2020185
DO - 10.3934/cpaa.2020185
M3 - Journal articles
AN - SCOPUS:85090760541
SN - 1534-0392
VL - 19
SP - 4143
EP - 4158
JO - Communications on Pure and Applied Analysis
JF - Communications on Pure and Applied Analysis
IS - 8
ER -