With the rapid development of computers and computing techniques, some increasingly complicated computational problems in engineering and science deserve further review and improvement. This work calculated the solution to the problem of Richards partial differential equation with its corresponding initial and boundary condition for one-dimensional unsaturated water movement in soil with changing bulk density by adopting an explicit backward difference method, an implicit forward difference method and an implicit central difference method. Therefore, a temporal-spatial distribution of water content in the process of filtration, evaporation and redistribution of water moisture within the soil column was obtained. Then the computational results were compared and verified, alternatively, by three methods, with a semi-analytical solution. This indicates the methods presented are of high validity, efficiency and accuracy. These methods were used for the first time for the modelling and prediction of the complicated water movement process in soil of changing bulk density. The computations show that the explicit method features a simpler formulation and more capability for complicated modelling, and the authors strongly recommend this method for application in time-related problems. In addition, this work innovatively developed a combination procedure of an implicit difference method and iterative solution method of a large set of linear algebraic equations. It not only avoids solving a large set of linear algebraic equations but also is able to be applied to complicated modelling of soil moisture profiles. Finally, the numerical methods and the technical skills presented in this work can be generalised for two-dimensional or three-dimensional soil moisture movement and more complicated water movement modeling.