Numerical method for particle acceleration in shocks

We have developed a reasonably fast and robust code to solve the standard Diffusion-Convection Equation, in plane parallel geometry, with synchrotron losses included. Standard iterative algorithms are rather inefficient for the solution of this equation: 1. they are time consuming, and convergence is not guaranteed in all cases; 2. the distribution is not adequately determined at levels much lower than its maximum value. We devised a completely different kind of approach for solving the finite difference equation. It does not require iterations, but is based on the solution of a linear system of equations. The number of operations required is of order of the cube of the grid size. We present the description of the numerical code, and some examples with different velocity profiles and levels of synchrotron losses.