Thesis Details
Vícenásobné integrály
The problem of definite integral and differential equation computation is still a significant part of many scientific branches and the solution of integral calculus tasks can be found in many industrial fields too. During the computation of such tasks, the accuracy and high-speed requirements are often confronted. These requirements are crucial during the process of the suitable method choice. The aim of this thesis is to propose, describe, implement and test a new numerical method, which combines the solution of definite integrals by transforming them into differential equations solved by the Taylor series with the traditional methods, which use the Newton-Cotes formulas. As a result, a new application has been developed, that provides fast results of definite two-dimensional integrals and reaches at least the precision of MATLAB. The major accomplishment of this thesis is the development of a new numerical method and its comparison to other established ways of computation.
finite integral, numerical methods, numerical integration, Newton-Cotes formulas, Taylor polynomial, multiple-precision arithmetic, TKSL/C, high-precision computation
Bidlo Michal, doc. Ing., Ph.D. (DCSY FIT BUT), člen
Chudý Peter, doc. Ing., Ph.D. MBA (DCGM FIT BUT), člen
Křivka Zbyněk, Ing., Ph.D. (DIFS FIT BUT), člen
Novák Michal, doc. RNDr., Ph.D. (DMAT FEEC BUT), člen
@bachelorsthesis{FITBT20093, author = "Nikola Vale\v{s}ov\'{a}", type = "Bachelor's thesis", title = "V\'{i}cen\'{a}sobn\'{e} integr\'{a}ly", school = "Brno University of Technology, Faculty of Information Technology", year = 2017, location = "Brno, CZ", language = "czech", url = "https://www.fit.vut.cz/study/thesis/20093/" }