We consider the Lax representation of the new two-component coupled integrable system recently discovered by the author. Connection of the hierarchy of infinitely many Lax pairs with each other is presented.

In this paper, we propose a high order residual distribution conservative finite difference scheme for solving steady state hyperbolic conservation laws on non-smooth Cartesian or other structured curvilinear meshes. WENO (weighted essentially non-oscillatory) integration is used to compute the numerical fluxes based on the point values of the solution, and the principles of residual distributi...

In this paper, a new scheme of arbitrary high order accuracy in both space and time is proposed to solve hyperbolic conservative laws. Based on the idea of flux vector splitting(FVS) scheme, we split all the space and time derivatives in the Taylor expansion of the numerical flux into two parts: one part with positive eigenvalues, another part with negative eigenvalues. According to a Lax-Wendr...

To guarantee the correction of numerical simulation programs implementing the fi-nite element method, it is necessary to formalize the mathematical notions and results that allowto establish the soundness of the method. The Lax-Milgram theorem is one of those theoreticalcornerstones: under some completeness and coercivity assumptions, it states existence and unique-ness of the s...

It is shown that for quasi-linear hyperbolic systems of the conservation form Wt = —Fx = —AWX, it is possible to build up relatively simple finite-difference numerical schemes accurate to 3rd and 4th order provided that the matrix A satisfies commutativity relations with its partial-derivative-matrices. These schemes generalize the Lax-Wendroff 2nd order scheme, and are written down explicitly....

A 3-D model for atmospheric pollutant transport is proposed considering a set of coupled convection–diffusion–reaction equations. The convective phenomenon is mainly produced by a wind field obtained from a 3-D mass consistent model. In particular, the modelling of oxidation and hydrolysis of sulphur and nitrogen oxides released to the surface layer is carried out by using a linear module of ch...

Methods We propose a numerical framework for determining pressure field in large arteries, the main components of which are: axi-symmetric 1-D unsteady wave-propagation model with elastic walls and an optimization framework for model personalization via parameter estimation from measured flow and anatomical data (Fig 1). 4D PC MRI data was acquired using a multi-slice phase contrast FLASH cine ...

Liftings of endofunctors on sets to relations are commonly used capture bisimulation coalgebras. Lax versions have been in those cases where strict lifting fails bisimilarity, as well modeling other notions simulation. This paper provides tools for defining and manipulating lax liftings. As a central result, we define notion distributive law functor over the powerset monad, show that there is a...

A three-step method due to Nijhoff and Bobenko & Suris to derive a Lax pair for scalar partial difference equations (P Es) is reviewed. The method assumes that the P Es are defined on a quadrilateral, and consistent around the cube. Next, the method is extended to systems of P Es where one has to carefully account for equations defined on edges of the quadrilateral. Lax pairs are presented for ...