Abstract This paper is devoted to the numerical analysis of non-smooth ensemble optimal control problems governed by Liouville (continuity) equation that have been originally proposed R.W. Brockett with purpose determining an efficient and robust strategy for dynamical systems. A methodology solving these presented based on a Lagrange optimization framework where controls are characterized as s...

We consider the solution of delay differential equations (DDEs) by using boundary value methods (BVMs). These methods require the solution of one or more nonsymmetric, large and sparse linear systems. The GMRES method with the Strang-type block-circulant preconditioner is proposed for solving these linear systems. We show that if a Pk1,k2 -stable BVM is used for solving an m-by-m system of DDEs...

In this paper, we propose a semi-Lagrangian finite difference formulation for approximating conservative form of advection equations with general variable coefficients. Compared with the traditional semi-Lagrangian finite difference schemes [4, 21], which approximate the advective form of the equation via direct characteristics tracing, the scheme proposed in this paper approximates the conserv...

We consider a class of second-order Strang splitting methods for Allen-Cahn equations with polynomial or logarithmic nonlinearities. For the case both linear and nonlinear propagators are computed explicitly. show that this type scheme is unconditionally stable regardless time step. Moreover we establish strict energy dissipation judiciously modified which coincides classical up to $\mathcal O(...

Abstract Many astrophysical environments involve convective or explosive flows driven by thermonuclear reactions (Type Ia supernovae, classical novae, X-ray bursts, stellar evolution). Simulation codes need to accurately capture the interactions between and hydrodynamics produce realistic models of these events. For reacting flows, operator splitting is commonly used couple reactions. Each proc...

One major goal of face-to-face restorative justice (RJ) is to help heal the psychological harm suffered by crime victims (Braithwaite, 2002). Substantial evidence from randomized controlled trials (RCTs) has shown that this can be accomplished (Strang, 2002) and more trials are underway (Sherman & Strang, 2004). These outcomes are even more clearly, if less rigorously, demonstrated through retr...

We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation which the solutions can be obtained in fixed number forward backward alternating substitutions. The use novel combination implicit explicit time discretizations one-dimensional case Strang splitting method several dimensional case. are described equati...

Motivated by an expression Persson and Strang on integral involving Legendre polynomials, stating that the square of $P_{2n+1}(x)/x$ integrated over $[-1,1]$ is always $2$, we present analog results for Hermite, Chebyshev, Laguerre Gegenbauer polynomials as well original polynomial with even index.