This paper extends the gas-kinetic scheme for one-dimensional inviscid shallow water equations (J. Comput. Phys. 178 (2002), pp. 533-562) to multidimensional gas dynamic equations under gravitational fields. Four important issues in the construction of a well-balanced scheme for gas dynamic equations are addressed. First, the inclusion of the gravitational source term into the flux function is ...

“Are there management tools that professionals use in business that academics have used successfully in higher education? The answer to that question is yes, and the balanced scorecard (BSC) is one such tool” (Beard, 2009, p. 275). Beard refers to applying BSC in U.S. universities (and her review is insightful for practitioners). To that end, this case study similarly discusses a balanced score...

The semi-implicit leapfrog time-discretization is a workhorse algorithm for initial-value MHD codes to bridge between vastly separated time scales. Inclusion of atomic interactions with neutrals breaks the functional structure equations that exploited by leapfrog. We address how best integrate physics into Following Crank-Nicolson method, one approach time-center in linear solver and use Newton...

A rigorous convergence analysis of the Strang splitting algorithm for Vlasov-type equations in the setting of abstract evolution equations is provided. It is shown that, under suitable assumptions, the convergence is of second order in the time step τ . As an example, it is verified that the Vlasov–Poisson equations in 1+1 dimensions fit into the framework of this analysis. Further, numerical e...

In this paper, we suggest a technique to avoid order reduction in time when integrating reaction-diffusion boundary value problems under non-homogeneous boundary conditions with exponential splitting methods. More precisely, we consider Lie-Trotter and Strang splitting methods and Dirichlet, Neumann and Robin boundary conditions. Beginning from an abstract framework in Banach spaces, a thorough...

Abstract Improved uniform error bounds on time-splitting methods are rigorously proven for the long-time dynamics of weakly nonlinear Dirac equation (NLDE), where nonlinearity strength is characterized by a dimensionless parameter $\varepsilon \in (0, 1]$. We adopt second-order Strang splitting method to discretize NLDE in time, and combine with Fourier pseudospectral space full-discretization....

This article focuses on the numerical solution of a classical, irreversible Gray Scott reaction-diffusion system describing kinetics simple autocatalytic reaction in an unstirred ow reactor. A novel finite element scheme based B-spline collocation method is developed to solve this model. Before applying method, "strang splitting" idea especially popularized for PDEs...

We consider the shift-invariant space, S((), generated by a set = f 1 ; : : : ; r g of compactly supported distributions on IR when the vector of distributions := (1 ; : : : ; r) T satisses a system of reenement equations expressed in matrix form as = X 2ZZ a()(2 ?) where a is a nitely supported sequence of r r matrices of complex numbers. Such multiple reenable functions occur naturally in the...

We give a uniied approach to error estimates for periodic interpolation on full and sparse grids in certain Sobolev spaces. We imposèperiodic' Strang{Fix conditions on the underlying functions in order to obtain error bounds with explicit constants. x1. Introduction The approximation and interpolation of bivariate periodic functions have been studied for some time. While periodic interpolation ...