The integration of the vlasov equation in configuration space

A convenient, fast, and accurate method of solving the one-dimensional Vlasov equation numerically in configuration space is described. It treats the convective terms in the x and v directions separately and produces a scheme of second order in Δt. The resulting free-streaming and accelerating equations are computed with Fourier interpolation and spline interpolation methods respectively. The numerical method is tested witth linear and nonlinear problems. The method is very accurate and efficient. A new method of smoothing the distribution function is given. It reduces the computational effort by artificially increasing the entropy of the system. As a result, the distribution function is smooth enough to be well represented on a given mesh. The methods can be generalized in a straightforward way to deal with more complicated cases such as problems with nonperiodic spatial boundary conditions, two- and three-dimensional problems with and without external magnetic and/or electric fields.