The aim of this paper is to present a new method and the tool validate numerical results Volterra integral equation with discontinuous kernels in linear non-linear forms obtained from Adomian decomposition method. Because disadvantages traditional absolute error show accuracy mathematical methods which based on floating point arithmetic, we apply stochastic arithmetic condition study efficiency...

The polynomial spline collocation method is proposed for solution of Volterra integral equations the first kind with special piecewise continuous kernels. Gausstype quadrature formula used to approximate integrals during discretization projection method. estimate accuracy obtained. Stochastic arithmetics also based on Controle et Estimation Stochastique des Arrondis de Calculs (CESTAC) and Cont...

Numerical simulation is used more and more frequently in the analysis of physical phenomena. A simulation requires several phases. The first phase consists of constructing a physical model based on the results of experimenting with the phenomena. Next, the physical model is approximated by a mathematical model. Generally, the mathematical model contains algebraic expressions, ordinary or partia...

Quantifying errors and losses due to the use of Floating-point (FP) calculations in industrial scientific computing codes is an important part Verification, Validation, Uncertainty Quantification process. Stochastic Arithmetic one way model estimate FP accuracy, which scales well large, codes. It exists different flavors, such as CESTAC or MCA, implemented various tools CADNA, Verificarlo, Verr...

Interval arithmetic and stochastic arithmetic have been both developed for the same purpose, i. e. to control errors coming from floating point arithmetic of computers and validate the results of numerical algorithms performed on computers. Interval arithmetic delivers guaranteed bounds for numerical results but requires special analysis and algorithms. On the other hand stochastic arithmetic i...

The researchers aimed to study the nonlinear fractional order model of malaria infection based on Caputo-Fabrizio derivative. homotopy analysis transform method (HATM) is applied floating-point arithmetic (FPA) and discrete stochastic (DSA). In FPA, show accuracy we use absolute error which depends exact solution a positive value ?. Because in real life problems do not have optimal ?, need intr...

Risk-taking related to road mobility of vulnerable users can be different from one country another, culture another. Vulnerable (pedestrians, cyclists and motorcyclists), who are those whose exterior protections most lacking compared drivers cars or trucks, constitute almost half the individuals killed in accidents (WHO, 2015). Contexts, cultural values beliefs likely play a role risk taking (C...

One of the considerable discussions for solving the nonlinear equations is to find the optimal iteration, and to use a proper termination criterion which is able to obtain a high accuracy for the numerical solution. In this paper, for a certain class of the family of optimal two-point methods, we propose a new scheme based on the stochastic arithmetic to find the optimal number of iterations in...