Stability and approximation of solutions in new reproducing kernel
Hilbert spaces on a semi-infinite domain
Abstract
We introduce new reproducing kernel Hilbert spaces on a trapezoidal
semi-infinite domain $B_{\infty}$ in the plane. We
establish uniform approximation results in terms of the number of nodes
on compact subsets of $B_{\infty}$ for solutions to
nonhomogeneous hyperbolic partial differential equations in one of these
spaces,
$\widetilde{W}(B_{\infty})$.
Furthermore, we demonstrate the stability of such solutions with respect
to the driver. Finally, we give an example to illustrate the efficiency
and accuracy of our results.