numerical solution

Fractional derivative model for tumor cells and immune system competition

Modeling a dynamics of complex biologic disease such as cancer still present a complex dealing.  So, we try in our case to study it by considering the system of normal cells, tumor cells and immune response as mathematical variables structured in fractional-order derivatives equations which express the dynamics of cancer's evolution under immunity of the body.  We will analyze the stability of the formulated system at different equilibrium points.  Numerical simulations are carried out to get more helpful and specific outcome about the variations of the cancer's dynamics.

Знаходження розв'язку нелінійної задачі теплопровідності з використанням випаровування для інтенсифікації тепловідведення

The non-linear model of the transient heat exchange process in a heat dissipation plate of a microelectronic device, heat from which is dissipated due to evaporation from it’s surface, has been built. The numerical solution of the non-linear model problem has been obtained by the Newton-Kantorovych method. Changes of temperature field in time and evaporation influence on the heat dissipation process have been investigated.