The time-dependent Smoluchowski equation is solved numerically by variational methods, for general boundary conditions and an initial Gaussian distribution function. The time and space conditions of the stability of the algorithm are discussed. The survival probability and scavenging probability of the solvated electron are computed. The numerical results are then compared with recent experiments on the solvated electron and biphenyl anion yields in amines and hydrazine. For liquids in which the rate constant for recombination between the solvated electron and the cation is high, the model applies and gives reasonable values for the mean initial separation distance anti r of the electron-cation pairs (anti r = 40 +- 10 A in ethylamine and 50 +- 10 A in n-propylamine). For other liquids such as ethylenediamine and hydrazine, it is shown that a competitive reaction of the solvated electron with a radical has to be taken into account to fit the experimental data concerning the nonhomogeneous decay of the solvated electron.