We study the Demand Adjustment Problem (DAP) associated to the urban traffic planning. The framework for the formulation of the DAP is mathematical programming with equilibrium constraints. In particular, if we consider the optimization problem equivalent to the equilibrium problem, the DAP...

The Forward-Backward Sweep Method is a numerical technique for solving optimal control problems. The technique is one of the indirect methods in which the differential equations from the Maximum Principle are numerically solved. After the method is briefly reviewed, two convergence theorems are...

Mathematical model of vertical electrical sounding by using resistivity method is studied. The model leads to an inverse problem of determination of the unknown leading coefficient (conductivity) of the elliptic equation in R2 in a slab. The direct problem is obtained in the form of mixed BVP in...

Utility-maximizing consumption and investment strategies in closed form are unknown for realistic settings involving portfolio constraints, incomplete markets, and potentially a high number of state variables. Standard numerical methods are hard to implement in such cases. We propose a numerical...

This paper deals with the construction of reliable numerical solutions of mixed problems for hyperbolic second order partial differential models with random information in the variable coefficients of the partial differential equation and in the initial data. Using random difference schemes a...

Avascular tumor growth model for multicellular spheroids is considered. The model is a moving boundary problem and consists of three types of cells. The governing equations are nonlinear hyperbolic and/or parabolic differential equations. Comparisons of the numerical solutions with the solution...

In this paper we construct and develop two competitive implicit finite difference scheme for a deterministic mathematical model associated with the evolution of influenza A disease in human population. Qualitative dynamics of the model is determined by the basic reproduction number, R0....

This paper presents a discrete numerical method for computing mean square approximations of random diffusion models. Mean square consistency of the random difference scheme is established. Sufficient conditions for the mean square stability of the proposed numerical solution are given.

In this article we consider how the operator of an electric power system should activate bids on the regulating power market in order to minimize the expected operation cost. Important characteristics of the problem are reaction times of actors on the regulating market and ramp-rates for...