Digital Approximations for Pseudo-Differential Equations and Error Estimates

On Discrete Solutions for Elliptic Pseudo-Differential Equations

“…For our case we need to apply any kind of cubature formulas for calculating the latter integral and a cubature formula for calculating the Fourier transformṽ(ξ). For v ∈ S(R m ) the discrete solution u d (x) tends to u(x) very fast under h → 0 [12].…”

“…In our opinion there is a reason to study discrete objects initially and then to apply their properties for studying approximation of starting continuous objects. This approach was started from papers [5][6][7][8][9][10] and further it was developed in [11][12][13][14][15]. We based on Eskin's approach for elliptic model pseudo-differential equations in a half-space [5] and have developed appropriate discrete theory.…”