On an operational matrix method based on generalized Bernoulli polynomials of level m

An operational matrix method based on generalized Bernoulli polynomials of level m is introduced and analyzed in order to obtain numerical solutions of initial value problems. The most innovative component of our method comes, essentially, from the introduction of the generalized Bernoulli polynomia...

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Bibliographic Details
Published inCalcolo Vol. 55; no. 3; pp. 1 - 29
Main Authors Quintana, Yamilet, Ramírez, William, Urieles, Alejandro
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.09.2018
Springer Nature B.V
Subjects
Boundary value problems
Conditioning
Mathematics
Mathematics and Statistics
Numerical Analysis
Polynomials
Theory of Computation
Ill-conditioned linear systems
11C08
11B83
33B99
65L80
Generalized Bernoulli polynomials of level
Operational matrix
Bernoulli polynomials
Galerkin method
41A50
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Summary:An operational matrix method based on generalized Bernoulli polynomials of level m is introduced and analyzed in order to obtain numerical solutions of initial value problems. The most innovative component of our method comes, essentially, from the introduction of the generalized Bernoulli polynomials of level m , which generalize the classical Bernoulli polynomials. Computational results demonstrate that such operational matrix method can lead to very ill-conditioned matrix equations.
ISSN:0008-0624
1126-5434
DOI:10.1007/s10092-018-0272-5