Numerical Computations for One Class of Dynamical Mathematical Models in Quasi-Sobolev Space

Abstract

The article studies some mathematical models that represent one class of dynamical equations in quasi-Sobolev space. The analytical investigation of solvability of the Cauchy problem in the quasi-Sobolev space and theoretical results used to enhance and develop an algorithm structure of the numerical procedures to find approximate solutions for models, the steps of algorithm based on the theoretical investigation of models, new algorithm of numerical method allowing to find approximate solutions of mathematical models under study in quasi-Sobolev space. Construction a program implements an algorithm of numerical method that allow finding approximate solutions for models. To construct the theory of degenerate holomorphic semigroups of operators in quasi-Banach spaces of sequences, we used the classical methods of functional analysis, theory of linear bounded operators, spectral theory. To construct the operators of resolving semigroups we used the Laplace transform of operator-valued functions in quasi-Banach spaces of sequences. The numerical investigation for models generate some approximate solutions which are normally based on the modified projection method. The convergence of the approximate solution to the exact one theoretically is justified by the convergence of the corresponding series, the agreement of approximate computations with the theoretical solution is established.