The regularization method is one of the important schemes to solve the ill-posed problems.
In this work, by combining the Wazwaz's regularization method and the homotopy analysis …

The aim of this paper is to apply the stochastic arithmetic to evaluate an improper integral by
using the Gauss-Laguerre integration rule. For this purpose, the CESTAC1 method and …

Floating-point arithmetic precision is limited in length the IEEE single (respectively double)
precision format is 32-bit (respectively 64-bit) long. Extended precision formats can be up to …

In this study we consider linear and nonlinear Volterra integral equations (VIEs) of the
second kind with discontinuous kernel. A novel iterative method using floating point …

The goal of this work is to apply the discrete stochastic arithmetic (DSA) and the fuzzy
CESTAC (Controle et Estimation Stochastique des Arrondis de Calculs) method to validate …

Differences in simulation results may be observed from one architecture to another or even
inside the same architecture. Such reproducibility failures are often due to different rounding …

We present in this paper a process which is suitable for the complete analysis of the
numerical quality of a large industrial scientific computing code. Random rounding, using …

The analysis of Floating-Point-related issues in HPC codes is becoming a topic of major
interest: parallel computing and code optimization often break the reproducibility of …

The analysis of Floating-Point-related issues in HPC codes is becoming a topic of major
interest. First, parallel computing and code optimization often break the reproducibility of …

Several approximations occur during a numerical simulation: physical effects mapy be
discarded, continuous functions replaced by discretized ones and real numbers replaced by …