Abstract We consider linear partial differential equations on resistance spaces that are uniformly elliptic and parabolic in the sense of quadratic forms involve abstract gradient divergence terms. Our main interest is to provide graph metric approximations for their unique solutions. For families with different coefficients a single compact space we prove solutions have accumulation points res...

The main focus of this paper is on efficiency analysis of two kinds of approximating functions (characteristic orthogonal polynomials and characteristic beam functions) that have been applied in the Rayleigh-Ritz method to determine the non-dimensional buckling and frequency parameters of an angle ply symmetric laminated composite plate with fully elastic boundaries. It has been observed that o...

The approximation of Euclidean QCD vertex functions Γ by a double sequence Γ is considered, where p is a perturbative order in g, and r the order of a rational approximation in the QCD scale Λ, non-analytic in g. Self-consistency of Γ in the Dyson-Schwinger equations comes about by a distinctive mathematical mechanism, which limits the self-consistency problem rigorously to the seven superficia...

We develop Stein’s method for $$\alpha $$ -stable approximation with \in (0,1]$$ , continuing the recent line of research by Xu (Ann Appl Probab 29(1):458–504, 2019) and Chen et al. (J Theor Probab, 2018. https://doi.org/10.1007/s10959-020-01004-1 ) in case (1,2)$$ . The main results include an intrinsic upper bound error a variant Wasserstein distance that involves characterizing differential ...

In this paper we propose a novel class of methods for high-order accurate integration multirate systems ordinary differential equation initial-value problems. The proposed construct schemes by approximating the action matrix $\varphi$ functions within explicit exponential Rosenbrock (ExpRB) methods, thereby called ExpRB (MERB) methods. They consist solution to sequence modified “fast” problems,...

We prove the global-in-time existence of large-data finite-energy weak solutions to an incompressible hybrid Vlasov-magnetohydrodynamic model in three space dimensions. The model couples three essential ingredients of magnetized plasmas: a transport equation for the probability density function, which models energetic rarefied particles of one species; the incompressible Navier–Stokes system fo...

A new method is introduced to design optimal tracking controllers for a general class of nonlinear systems. A recently developed recursive approximation theory is applied to solve the nonlinear optimal tracking control problem explicitly by classical means. This reduces the nonlinear problem to a sequence of linear-quadratic and time-varying approximating problems which, under very mild conditi...