Some remarks on discretisation of spatially invariant systems

摘要

The paper deals with discretisation of 2-D spatially invariant systems. Three different discretisation schemes are used - Tustin's approximation, backward difference scheme and Crank-Nicolson discretisation. Their properties and importance are discussed in the paper. As an example a heat conduction in a rod is considered. Its model discrete in both time and space is obtained using all the above mentioned difference schemes. To determine whether the discrete model converges to the solution, von Neumann analysis of stability is applied to each scheme. The system is stabilised with use of each of obtained discrete models. Numerical simulations are included. Experiments with changing the parameters of discretisation are also given.