This paper studies the second kind linear Volterra integral equations (IEs) with a
discontinuous kernel obtained from the load leveling and energy system problems. For …

In this paper, the nonlinear shallow water wave equation is illustrated. The famous semi-
analytical method, homotopy analysis method (HAM) is applied for solving this equation …

The type length chosen for floating-point numbers (eg 32 bits or 64 bits) may have an impact
on the execution time, especially on SIMD (Single Instruction Multiple Data) units …

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 …

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 …

The numerical result provided by an approximation method is affected by a global error,
which consists of both a truncation error and a round-off error. Let us consider the …

One of the schemes to find the optimal shape parameter and optimal number of points in the
radial basis function (RBF) methods is to apply the stochastic arithmetic (SA) in place of the …

Numerical integration is an operation that is frequently available in multiple precision
numerical software packages. The different quadrature schemes used are considered well …

Discrete Stochastic Arithmetic (DSA) estimates round-off error propagation in a program. It is
based on a synchronous execution of several instances of the program to control using a …

In this article, we show how to perform a dynamical control of Newton's method for the
computation of multiple roots of polynomials. Using Discrete Stochastic Arithmetic, root …