Open AccessComputation of Definite Integral Over Repeated Integral
Author(s) -
Katarína Tvrdá,
María Minárová
Publication year - 2018
Publication title -
tatra mountains mathematical publications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.171
H-Index - 12
eISSN - 1338-9750
pISSN - 1210-3195
DOI - 10.2478/tmmp-2018-0026
Subject(s) - mathematics , computation , improper integral , volume integral , multiple integral , integral equation , cauchy distribution , positive definite matrix , cauchy's integral formula , singular integral , mathematical analysis , numerical integration , gauss , focus (optics) , calculus (dental) , algorithm , cauchy problem , initial value problem , eigenvalues and eigenvectors , medicine , physics , dentistry , quantum mechanics , optics
The tasks involving repeated integral occur from time to time in technical practice. This paper introduces the research of authors in the field of repeated integrals within the required class of functions. Authors focus on the definite integral over repeated integral and they develop a tool for its computation. It involves two principal steps, analytical and numerical step. In the analytical step, the definite integral over a repeated integral is decomposed into n integrals and then the Cauchy form is used for further rearrangement. Numerical step involves Gauss type integration slightly modified by the authors. Several examples illustrating the operation of both analytical and numerical steps of the method are provided in the paper.