The MHD flows are governed by the Navier-Stokes equations coupled with the Maxwell equations through coupling terms. We prove the unconditional stability of a partitioned method for the evolutionary full MHD equations, at high magnetic Reynolds number, in the Elsässer variables. The method we propose is a defect correction second order scheme, and entails the implicit discretization of the subp...

This article shows that the unconditional stability of the Dual-Finite Volume Method, which is at least valid for linear problems, is not true for generic nonlinear differential equations including the PMEs unless the coefficient appearing in the numerical fluxes are appropriately evaluated. This article provides a theoretically truly isotone numerical fluxes specialized for solving the PMEs pr...

We devise and analyze a simple numerical method for the approximation of large bending isometries. The discretization employs a discrete Kirchhoff triangle to deal with second order derivatives and convergence of discrete solutions to minimizers of the continuous formulation is proved. Unconditional stability and convergence of an iterative scheme for the computation of discrete minimizers that...

We derive a new compact high-order finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth order accurate in space and second order accurate in time. To prove results on the unconditional stability in the sense of von Neumann we perform a thorough Fourier analysis of the problem and deduce convergence of our scheme. We present results of numerical exper...

The solution of fluid flows, modeled using the Navier-Stokes or Euler equations, fully coupled with structures/solids is considered. Simultaneous and partitioned solution procedures, used in the solution of the coupled equations, are briefly discussed, and advantages and disadvantages of their use are mentioned. In addition, a simplified stability analysis of the interface equations is presente...

Linear instability and nonlinear energy stability analyses are developed for the problem of a fluid-saturated porous layer stratified by penetrative thermal convection and two salt concentrations. Unusual neutral curves are obtained, in particular non-perfect ‘heartshaped’ oscillatory curves that are disconnected from the stationary neutral curve. These curves show that three critical values of...

Based on the concept of domain decomposition we construct a class of alternating group explicit method for fourth order parabolic equations. Furthermore, an exponential type alternating group explicit method for 2D convection-diffusion equations is derived, which is effective in convection dominant cases. Both of the two methods have the property of unconditional stability and intrinsic paralle...

In this paper we define unconditional stability properties of exponential Runge-Kutta methods when they are applied to semi-linear systems of ordinary differential equations characterized by a stiff linear part and a nonstiff non-linear part. These properties are related to a class of systems and to a specific norm. We give sufficient conditions in order that an explicit method satisfies such p...