A fast, approximative method for integrating the stochastic coalescence equation

The use of mean values of the drop number density in the coalescence equation is shown to lead to a system of ordinary differential equations that provide good approximative solutions with a minimum of computational effort. The coefficients in this system of equations are functions of the kernel and can be obtained by simple quadrature. Comparisons are made between numerical and analytic solutions for two types of kernels (constant and sum of arguments), using a Gaussian initial distribution of cloud droplets. Systematic deviations of the numerical results from corresponding analytic solutions are shown to depend on the choice of variables, and methods to suppress these deviations are discussed.