In the article, to solve the problem of assessing the information impact on the electorate during election campaigns, algorithmic solutions, including a mathematical model, a numerical scheme and algorithmic implementations, are formed. This assessment is reduced to determining the instantaneous values of the number of voters who prefer a candidate (party), taking into account: the positive or negative stochastic nature of the impact of mass media; interpersonal interaction; two-step assimilation of information; the presence of a variety of mass media, social groups and a list of candidates. The mathematical model is based on a generalized model of information confrontation in a structured society and, with the introduction of stochastic components in the intensity of agitation, it is reduced to solving the FokkerPlanckKolmogorov equation. For its study in the formulation of the Galerkin method, a numerical scheme is proposed and the order of its convergence is determined. In relation to the basic procedures of the numerical scheme, the features of the algorithmic implementation are clarified.
A numerical scheme for nonlinear hyperbolic evolution equations is made based on the implicit Runge-Kutta method and the Fourier spectral method. The detailed discretization processes are discussed in the case of one-dimensional Klein-Gordon equations. In conclusion, a numerical scheme with third-order accuracy is presented. The order of total calculation cost is O(Nlog2N). As a benchmark, the relations between numerical accuracy and discretization unit size and that between the stability of calculation and discretization unit size are demonstrated for both linear and nonlinear cases.
The analysis of nanofluid dynamics in a bounded domain attained much attention of the researchers, engineers, and industrialists. These fluids became much popular in the researcher’s community due to their broad uses regarding the heat transfer in various industries and fluid flowing in engine and in aerodynamics as well. Therefore, the analysis of Cu-kerosene oil and Cu-water is organized between two Riga plates with the novel effects of thermal radiations and surface convection. The problem reduced in the form of dimensionless system and then solved by employing variational iteration and variation of parameter methods. For the sake of validity, the results checked with numerical scheme and found to be excellent. Further, it is examined that the nanofluids move slowly by strengthen Cu fraction factor. The temperature of Cu-kerosene oil and Cu-water significantly rises due to inducing thermal radiations and surface convection. The behaviour of shear stresses is in reverse proportion with the primitive parameters, and local Nusselt number increases due to varying thermal radiations, Biot number, and fraction factor, respectively.
AbstractIn the context of coupling hyperbolic problems, the maximum stable time step of an explicit numerical scheme may depend on the design of the coupling procedure. If this is the case, the coupling procedure is sensitive to changes in model parameters independent of the Courant–Friedrichs–Levy condition. This sensitivity can cause artificial stiffness that degrades the performance of a numerical scheme. To overcome this problem, we present a systematic and general procedure for weakly imposing coupling conditions via penalty terms in a provably non-stiff manner. The procedure can be used to construct both energy conservative and dissipative couplings, and the user is given control over the amount of dissipation desired. The resulting formulation is simple to implement and dual consistent. The penalty coefficients take the form of projection matrices based on the coupling conditions. Numerical experiments demonstrate that this procedure results in both optimal spectral radii and superconvergent linear functionals.