Mathematical model of growing tumor

Abstract

The mathematical model of malignant tumor, which represents itself an initial boundary task for system of differential equations in partial derivatives, has been developed. In model there are 3 types of cells, which interact between each other, it is a dividing, normal and dead cells. An inhibiting influence of cells at each other is considered in that way that the growth of continuously dividing cells is accompanied by destruction of normal cells and emergence of dead cells. Analysis of stability of stationary decisions has been done. Evaluation of velocity of distribution tumor on a straight line has been given.

An embedded fourth order method for solving structurally partitioned systems of ordinary differential equations

“…Such systems appear, for example, in problems of optimal control and stabilisation [7,8], medical modelling [13], celestial mechanics or high-energy physics. For instance, large-scale oscillations of systems with rotational symmetry [6] are described (after some reducing) with equations…”

Mathematical modeling of the system of drilling rig

“…Figure 5 presents absolute displacement in the plane XY. The comparison of the results was performed with the numerical results that are obtained by solving the Cauchy problem for systems of differential equations using numerical method of Dormand-Prince [17], which considers structural features of the equations [18], and can be successfully used for solving differential equations in partial derivatives [19][20][21]. The difference between the maximum deviations is less than 2%.…”

On the equation of fourth order with quadratic nonlinearity

“…For the construction of solutions of nonlinear differential equations in partial derivatives [6][7][8][9][10][11][12] is used different analytical and numerical methods: the perturbation methods, the small parameter method, the separation of variables method, the linearization method, the averaging method, the method of the stretched coordinates, the method of composite expansions, grid methods -the method of finite differences and the finite element method [13][14][15][16][17][18][19].…”