Computational experiment for one class of evolution mathematical models in quasi-Sobolev spaces

In the article the mathematical model representing one class of evolution equations in quasi-Banach spaces is studied. A theorem on the unique solvability of the Cauchy problem is stated. The conditions for the phase space existence are presented. We also give the conditions for exponential dichotomies of solutions. Based on the theoretical results there was developed an algorithm for the numerical solution of the problem. The algorithm is implemented in Maple. The article includes description of the algorithm which is illustrated by variety of model examples showing the work of the developed program and represent the main properties of solutions.