The goal of the research was to construct a model for calculating the Tourism Development Index (TDI) at the local level. TDI is based on ten indicators: total number of beds, total number of beds per 100 residents, number of beds in hotels and similar establishments, number of beds in hotels and similar establishments per 100 residents, number of tourist arrivals, number of tourist arrivals per capita, number of overnight stays, number of overnight stays per capita, number of employed in tourism and hospitality and share of employed in tourism and hospitality in total employment. Based on TDI, 556 cities/towns and municipalities were categorised into five classes. Due to the usage of both absolute and relative values, TDI recognises the tourism development better than the previously used indices.

A novel derivative-free algorithm for solving quasilinear systems is presented. It resembles "classical" optimization approach but greatly simplifies computation, resulting in fast execution and numerical stability. Though the global convergence cannot be guaranteed, it turns out that the presented algorithm finds a solution as successfully as other commonly accepted methods. The algorithm is clearly developed and mathematically founded, and its properties are examined by comparisons with other methods.

Tension spline is a function that, for given partition x0 < x1 < . . . < xn, on each interval [xi, xi+1] satisfies differential equation (D 4 − ρ 2i D 2 )u = 0, where ρi's are prescribed nonnegative real numbers. In the literature, tension splines are used in collocation methods applied to two-points singularly perturbed boundary value problems with Dirichlet boundary conditions.In this paper, we adapt collocation method to solve a time dependent reactiondiffusion problem of the formwith Dirichlet boundary conditions. We tested our method on the time-uniform mesh with Nx N N × Nt N N elements. Numerical results show ε-uniformly convergence of the method.

No abstract