The Euler–Lagrange Approximation of the Mean Field Game for the Planning Problem

Mean field game for modeling of COVID-19 spread

“…The numerical algorithm considered in this paper is based on the ideas proposed in the works [14][15][16][17] and modified for application to the problems of epidemiology. The algorithm gives a direct and simply rule for minimizing the cost functional, ensures the fulfillment of the law of conservation of the entire mass of agents, and allows to take into account more complex functions F i (α, t, x) responsible for control, instead of the traditionally used quadratically dependent on α [11].…”

“…To construct a computational scheme for equations (8), modify the idea firstly proposed by prof. Shaydurov V.V. for numerical solution of FPK equation ( 5) and applied to various MFG statements in [14][15][16][17]. The idea was to split the approximation of the FPK (5) equation into two parts: advection and diffusion one.…”

“…Following the idea proposed in [14][15][16][17] get the approximation for (31) in the point t k, x i+1/2 as…”

Approximate Methods for Solving Differential Equations for Continuous Models of a Sustainable Economy

“…In [12] the authors studied demand forecasting, a model based on stochastic differential equations. It may also be noted that in addition to continuous models of the economy based on linear differential equations and their systems, there are also two-dimensional models, such as, [13,14], which involve partial differential equations, but we will focus only on ordinary linear differential equations, the range of coverage of economic models which are diverse. For processes accompanied by jumps, differential equations of fractional order of differentiation are used, economic problems with jumps refer to the problems of sustainable economy.…”