Higher order approximation methods for the Boltzmann equation. (English) Zbl 0905.65134

Ohwada, Taku

J. Comput. Phys. 139, No. 1, 1-14 (1998).

The paper deals with a higher-order time difference method for the spatially nonhomogeneous Boltzmann equation \[ \begin{split} {\partial f\over \partial t}(X,\xi,t) +\xi \cdot {\partial f\over \partial X} (X,\xi,t) =Q\bigl(f(X, \xi,t), f(X,\xi,t) \bigr) [\xi],\\ 0<t\leq \Delta t, \quad f(X,\xi,0) =f_0(X,\xi). \end{split} \] The proposed method consists of two steps, as the first one is the same as the convection step in the splitting method while the second one takes into account not only the collision term but also its variation along the characteristic line.

Reviewer: E.Minchev (Sofia)

MSC:

65R20	Numerical methods for integral equations
45K05	Integro-partial differential equations

Keywords:

finite difference method; higher-order accuracy; time difference method; Boltzmann equation; splitting method

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