Keywords: Compact schemes Finite difference method Burgers' equation Low-storage Runge–Kutta scheme a b s t r a c t A numerical solution of the one-dimensional Burgers' equation is obtained using a sixth-order compact finite difference method. To achieve this, a tridiagonal sixth-order compact finite difference scheme in space and a low-storage third-order total variation diminishing Runge–Kutt...

In this paper, a two-dimensional cellular automaton(CA) associated with a two-dimensional Burgers equation is presented. The 2D Burgers equation is an integrable generalization of the well-known Burgers equation, and is transformed into a 2D diffusion equation by the Cole-Hopf transformation. The CA is derived from the 2D Burgers equation by using the ultradiscrete method, which can transform d...

Wick calculus in Gaussian analysis is investigated. It is shown that this calculus can be developed in a space of regular generalized functions. The results are applied to the discussion of solutions for Wick type stochastic (partial) diierential equations. In particular, the viscous Burgers equation with a stochastic source is studied. Its solution is shown to be a regular generalized process ...

The simplest equation method presents a wide applicability to handling nonlinear wave equations. In this paper, we establish travelling wave solutions for some nonlinear evolution equations. The simplest equation method is used to construct the travelling wave solutions of new Hamiltonian amplitude equation, (3 + 1)-dimensional generalized KP equation, Burgers-KP equation, coupled Higgs field e...

By means of three fundamental structures we can define, in a general way, a sheaf A of differential algebras containing most of the special cases met in the theory of generalized functions. A convenient choice of these structures permits us to study Burgers’ equation with δ-Dirac measure as initial data, and we can construct a generalized δ-shock wave as an approximate solution, self-similar to...