Improved error estimate for the valence approximation

Error Estimate for Godunov Approximation of Locally Constrained Conservation Laws

Error estimate for the diffusion approximation of the Wright--Fisher model.

The Wright--Fisher model and its approximating diffusion model are compared in terms of the expected value of a smooth but arbitrary function of nth-generation gene frequency. In the absence of selection, this expectation is shown to differ in the two models by at most a linear combination (with coefficients depending only on the derivatives of the smooth function involved) of the maximum mutat...

The Estimate for Approximation Error of Neural Network with Two Weights

The neural network with two weights is constructed and its approximation ability to any continuous functions is proved. For this neural network, the activation function is not confined to the odd functions. We prove that it can limitlessly approach any continuous function from limited close subset of R(m) to R(n) and any continuous function, which has limit at infinite place, from limitless clo...

An error estimate for the parabolic approximation of multidimensional scalar conservation laws with boundary conditions

We study the parabolic approximation of a multidimensional scalar conservation law with initial and boundary conditions. We prove that the rate of convergence of the viscous approximation to the weak entropy solution is of order η, where η is the size of the artificial viscosity. We use a kinetic formulation and kinetic techniques for initial-boundary value problems developed by the last two au...

A quasi-optimal error estimate for a discrete singularly perturbed approximation to the prescribed curvature problem

Solutions of the so-called prescribed curvature problem minA⊆Ω PΩ(A)− ∫ A g(x), g being the curvature field, are approximated via a singularly perturbed elliptic PDE of bistable type. For nondegenerate relative minimizers A ⊂⊂ Ω we prove an O( 2| log |2) error estimate (where stands for the perturbation parameter), and show that this estimate is quasi-optimal. The proof is based on the construc...