In the paper, differential quadrature method (DQM) is used to find numerical solutions of reaction-diffusion equations with different boundary conditions. The DQM-method changes the reaction- diffusion equation (ordinary differential equation) into a system of algebraic equations. The obtained system is solved using built-in procedures of Maple®(Computer Algebra System-type program). Calculations were performed with Maple®program. The test problems include reaction-diffusion equation applied in heterogeneous catalysis. The method can be employed even in relatively hard tasks (e.g. ill-conditioned, free boundary problems).

In the paper the practical stability problem for the discrete, non-integer order model of one dimmensional heat transfer process is discussed. The conditions associating the practical stability to sample time and maximal size of finite-dimensional approximation of heat transfer model are proposed. These conditions are formulated with the use of spectrum decoposition property and practical stability conditions for scalar, positive, fractional order systems. Results are illustrated by a numerical example.

The nonlinear interaction of wave and non-wave modes in a gas planar flow are considered. Attention is mainly paid to the case when one sound mode is dominant and excites the counter-propagating sound mode and the entropy mode. The modes are determined by links between perturbations of pressure, density, and fluid velocity. This definition follows from the linear conservation equations in the differential form and thermodynamic equations of state. The leading order system of coupling equations for interacting modes is derived. It consists of diffusion inhomogeneous equations. The main aim of this study is to identify the principle features of the interaction and to establish individual contributions of attenuation (mechanical and thermal attenuation) in the solution to the system.