Ternary diffusion models lead to strongly coupled systems of PDEs. We choose the smallest diffusion coefficient as a small parameter in a power series expansion whose components fulfill relatively simple equations. Although this series is divergent, one can use its finite sums to derive feasible numerical approximations, e.g. finite difference methods (FDMs).

Exchange traded funds (ETFs) are financial innovations that may be considered as a part of the index financial instruments category, together with stock index derivatives. The aim of this paper is to explore the trajectories and formulates predictions regarding the spread of ETFs on the financial markets in six European countries. It demonstrates ETFs’ development trajectories with regard to stock index futures and options that...

We consider structured population models with diffusion and dynamic boundary conditions. The respective approximation, called Rothe’s method, produces positive and exponentially bounded solutions. Its solutions converge to the exact solution of the original PDE.

We deal with a size-structured model with diffusion. Partial differential equations are approximated by a large system of ordinary differential equations. Due to a maximum principle for this approximation method its solutions preserve positivity and boundedness. We formulate theorems on stability of the method of lines and provide suitable numerical experiments.