A numerical solution of the breakthrough curve in column adsorption has been developed with the view to the stability, reliability and accuracy of the solution being the principal requirements. The methods used to attain this goal were the use of the implicit Euler method, the choice of the relation time step/length step so that a number of terms disappear, the use of the quadratic one-dimensional minimization method for the iteration of the concentration on the surface of the particle, and iteration of the average solid concentration at each location and time by substitution. The method has been tested by comparison with analytical solutions in the regions applicable, and found to be robust and accurate. However, the method developed is relatively time consuming because the whole of the time/location grid must be calculated and thus the extent of computation increases with the length of the column. For this reason, we have developed a method whereby the calculation starts with a standard numerical solution but a constant pattern is detected by the use of special numerical rules. When this constant pattern has been attained within the set accuracy, the advance of the concentration wave in the rest of the column is calculated analytically. It is shown that this procedure provides good accuracy and a considerable reduction in the computing time, particularly for longer columns.