A positive splitting method for mixed hyperbolic-parabolic systems (Q2712972)

A system of coupled hyperbolic-parabolic partial differential equations that arises frequently in biomathematical models is investigated. A method of lines approach to the numerical solution of this system is presented and for the resulting large system of stiff ordinary differential equations a splitting technique is used, the part arising from the hyperbolic equation is treated with an explicit method and the part from the parabolic equation with an implicit method. Special attention is given to preserve the positivity of the numerical solution of the partial differential equations. In order to achieve this, a flux limiter in the discretization of the hyperbolic equation is used. NEWLINENEWLINENEWLINEA numerical example of a biomathematical model describing tumor-induced angiogenesis is presented and results of this approach are compared with the results obtained by standard methods.