We study the stability of some finite difference schemes for symmetric hyperbolic systems in two space dimensions. For the so-called upwind scheme and the Lax-Wendroff scheme with a stabilizer, we show that stability is equivalent to strong stability, meaning that both schemes are either unstable or `-decreasing. These results improve on a series of partial results on strong stability. We also ...

A numerical scheme for a SIS epidemic model with a delay is constructed by applying a nonstandard finite difference (NSFD) method. The dynamics of the obtained discrete system is investigated. First we show that the discrete system has equilibria which are exactly the same as those of continuous model. By studying the distribution of the roots of the characteristics equations related to the lin...

Tasks. Implement the implicit finite difference scheme (i.e., backward Euler scheme) and the Crank-Nicolson scheme and compute the option prices in this way. Moreover, study the empirical convergence rates. You need to choose the following numerical parameters: • The truncation values for the infinite domain xmin < 0 < xmax. To simplify the analysis, you should use the same values for all the r...

Dendrites have voltage-gated ion channels which aid in production of action potentials. Thus dendrites are not just passive conductors of information, but actively act on the incoming input. Here we assume Hodgkin-Huxley formulations of voltage-gated ion channels on the dendrite. These equations are normally solved by some form of central difference scheme or the spectral methods. We use a comp...

Two-dimensional reactive Navier-Stokes equations are solved using a simple implicit Beam-Warming finite difference scheme. Comparisons of the detonation wave solutions of reactive Euler equations and reactive Navier-Stokes equations show that physical diffusion is important at high resolution when the numerical diffusion becomes negligible. Hence, for accurate detonation wave solutions it is ne...

We describe a novel method for the generation of tangent-linear code by augmentation of LL-parsers generated by the software tool ANTLR. The main advantage of this approach to source code augmentation is the missing requirement for an internal representation of the original program. We consider this work as the basis for further investigations into how far this technique can be extended in the ...

We present an accurate and efficient finite difference method for solving the Black–Scholes (BS) equationwithout boundary conditions. TheBS equation is a backward parabolic partial differential equation for financial option pricing and hedging. When we solve the BS equation numerically, we typically need an artificial far-field boundary condition such as the Dirichlet, Neumann, linearity, or pa...

For discontinuous solutions of hyperbolic conservation laws, a Hybrid scheme, based on the high order nonlinear characteristic-wise weighted essentially non-oscillatory conservative finite difference (WENO) scheme and the high resolution spectral-like linear compact finite difference (Compact) scheme, is developed for capturing shock and strong gradients accurately and resolving smooth scale st...