Results 11 to 20 of about 88 (59)
Validation of results of collocation methods for ODEs with the CADNA library
Applied Numerical Mathematics, 1996 International audienceThis paper shows the efficiency of collocation methods for integrating ordinary differential system when they are performed with an efficient round-off error analysis method. In a first part collocation methods are briefly presented
J Vignes
exaly +2 more sources
CADNA_C: A version of CADNA for use with C or C++ programs
Computer Physics Communications, 2010 International audienceThe CADNA library enables one to estimate round-off error propagation using a probabilistic approach. The CADNA_C version enables this estimation in C or C++ programs, while the previous version had been developed for Fortran ...
Jean-Luc Lamotte, Fabienne Jézéquel
exaly +2 more sources
A Valid Scheme to Evaluate Fuzzy Definite Integrals by Applying the CADNA Library
International Journal of Fuzzy System Applications, 2017 The aim of this paper is to estimate the value of a fuzzy integral and to find the optimal step size and nodes via the stochastic arithmetic. For this purpose, the fuzzy Romberg integration rule is considered as an integration rule, then the CESTAC ...
Mohammad Ali Fariborzi Araghi +1 more
exaly +2 more sources
Numerical ‘health check’ for scientific codes: the CADNA approach
Computer Physics Communications, 2007 Scientific computation has unavoidable approximations built into its very fabric. One important source of error that is difficult to detect and control is round-off error propagation which originates from the use of finite precision arithmetic.
Denis, C. +7 more
exaly +2 more sources
A Valid Dynamical Control on the Reverse Osmosis System Using the CESTAC Method
Mathematics, 2020 The aim of this study is to present a novel method to find the optimal solution of the reverse osmosis (RO) system. We apply the Sinc integration rule with single exponential (SE) and double exponential (DE) decays to find the approximate solution of the
Samad Noeiaghdam +4 more
doaj +2 more sources
Improving CADNA Performance on GPUs
, 2018 International audienceThe quantification of rounding errors is crucial for numerical simulations on massively parallel architectures such as GPUs. The CADNA library enables one to estimate rounding errors in simulation programs.
Julien Brajard, Fabienne Jézéquel
exaly +2 more sources
MathematicsThe primary objective of this study is to present a new technique and library designed to validate the outcomes of numerical methods used for addressing various issues.
Samad Noeiaghdam, Sanda Micula
doaj +2 more sources
Известия Иркутского государственного университета: Серия "Математика", 2022 The polynomial spline collocation method is proposed for solution of Volterra integral equations of the first kind with special piecewise continuous kernels.
Aleksandr Tynda +2 more
doaj +1 more source
An Integrated Genetic Algorithm and Homotopy Analysis Method to Solve Nonlinear Equation Systems
Mathematical Problems in Engineering, Volume 2021, Issue 1, 2021., 2021 Solving nonlinear equation systems for engineering applications is one of the broadest and most essential numerical studies. Several methods and combinations were developed to solve such problems by either finding their roots mathematically or formalizing such problems as an optimization task to obtain the optimal solution using a predetermined ...
Hala A. Omar, Muhammad Arif
wiley +1 more source
Numerical validation in quadruple precision using stochastic arithmetic [PDF]
, 2018 International audienceDiscrete Stochastic Arithmetic (DSA) enables one to estimate rounding errors and to detect numerical instabilities in simulation programs.
Lathuilière, Bruno +4 more
core +1 more source