Abst rac t . The Crank-Nicolson scheme is widely used to solve numerically the diffusion equation, because of its good stability properties. It is, however, ill-behaved when large time-steps are used: the short wave-lengths may happen to be less damped than the long ones. A detailed analysis of this flaw is performed and an Mternative scheme is proposed, which removes this difficulty while pres...

In this paper, we design a new class of central compact schemes based on the cell-centered compact schemes of Lele [S.K. Lele, Compact finite difference schemes with spectral-like resolution, J. Comput. Phys. 103 (1992) 16-42]. These schemes equate a weighted sum of the nodal derivatives of a smooth function to a weighted sum of the function on both the grid points (cell boundaries) and the cel...

Abstract. The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the numerical error is taken into account. The theoretical study of a related linear algebraic problem gives general results which can lead to the dete...

We give sufficient conditions under which solutions of discretized in space second-order parabolic and elliptic equations, perhaps degenerate, admit estimates of the first derivatives in the space variables independent of the mesh size.

In this paper, we primarily explore numerical solutions to the Quantum 1D Infinite Square Well problem, and the 1D Quantum Scattering problem. We use different finite difference schemes to approximate the second derivative in the 1D Schrodinger’s Equation and linearize the problem. By doing so, we convert the Infinite Well problem to a simple Eigenvalue problem and the Scattering problem to a s...

Perform numerical analysis of sound generation and propagation with accuracy and with lower computational time are some of the main challenges for Computational Aeroacoustics (CAA), which had experienced some major improvements in the last decade. In the present work it was performed numerical study of two-dimensional propagation of waves by solving LEE equations applied to a Gaussian pulse in ...

This article refers to algorithms based on finite difference schemes for computing mean and affine curvature evolutions of digital images, introduced by Alvarez and Morel [L. Alvarez, J.M. Morel, “Formalization and computational aspects of image analysis”, Acta Numerica, pp. 159, 1994]. We discuss consistency, stability and convergence. Our analysis focuses on some possible choices of the param...