On fully discrete Galerkin methods of second-order temporal accuracy for the nonlinear Schrödinger equation.
On Jeffreys model of heat conduction
The Jeffreys model of heat conduction is a system of two partial differential equations of mixed hyperbolic and parabolic character. The analysis of an initial-boundary value problem for this system is given. Existence and uniqueness of a weak solution of the problem under very weak regularity assumptions on the data is proved. A finite difference approximation of this problem is discussed as well. Stability and convergence of the discrete problem are proved.
On Large Eddy Simulation and Variational Multiscale Methods in the numerical simulation of turbulent incompressible flows
Numerical simulation of turbulent flows is one of the great challenges in Computational Fluid Dynamics (CFD). In general, Direct Numerical Simulation (DNS) is not feasible due to limited computer resources (performance and memory), and the use of a turbulence model becomes necessary. The paper will discuss several aspects of two approaches of turbulent modeling—Large Eddy Simulation (LES) and Variational Multiscale (VMS) models. Topics which will be addressed are the detailed derivation of these...
On multigrid for linear complementarity problems with application to American-style options.
On pricing American and Asian options with PDE methods.
On projection-difference analogues of the identity operator
On second order of accuracy difference scheme of the approximate solution of nonlocal elliptic-parabolic problems.
On some finite difference schemes for solution of hyperbolic heat conduction problems
We consider the accuracy of two finite difference schemes proposed recently in [Roy S., Vasudeva Murthy A.S., Kudenatti R.B., A numerical method for the hyperbolic-heat conduction equation based on multiple scale technique, Appl. Numer. Math., 2009, 59(6), 1419–1430], and [Mickens R.E., Jordan P.M., A positivity-preserving nonstandard finite difference scheme for the damped wave equation, Numer. Methods Partial Differential Equations, 2004, 20(5), 639–649] to solve an initial-boundary value problem...
On stability of some difference schemes for parabolic diffusion equation.
On stability of spline difference scheme for reaction-diffusion time-dependent singularly perturbed problem.
On the analysis of Bérenger’s perfectly matched layers for Maxwell’s equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This last...
On the analysis of Bérenger's Perfectly Matched Layers for Maxwell's equations
In this work, we investigate the Perfectly Matched Layers (PML) introduced by Bérenger [3] for designing efficient numerical absorbing layers in electromagnetism. We make a mathematical analysis of this model, first via a modal analysis with standard Fourier techniques, then via energy techniques. We obtain uniform in time stability results (that make precise some results known in the literature) and state some energy decay results that illustrate the absorbing properties of the model. This...
On the analytical and numerical treatment of a class of PDE's with the application to some two-valley semiconductor.
On the approximation of the dynamics of sandpile surfaces.
On the computation of roll waves
The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the numerical solution and yields false...
On the Computation of Roll Waves
The phenomenon of roll waves occurs in a uniform open-channel flow down an incline, when the Froude number is above two. The goal of this paper is to analyze the behavior of numerical approximations to a model roll wave equation ut + uux = u,u(x,0) = u0(x), which arises as a weakly nonlinear approximation of the shallow water equations. The main difficulty associated with the numerical approximation of this problem is its linear instability. Numerical round-off error can easily overtake the...
On the convergence of a factorized vector finite difference scheme.
On the convergence of a multicomponent alternating direction difference scheme.
On the Convergence Rate Estimates for Finite Difference Schemes Approximating Homogeneous Initial-boundary Value Problem for Hyperbolic Equation
On the derivation of the modified equation for the analysis of linear numerical methods