We introduce new reproducing kernel Hilbert spaces on a trapezoidal semi-infinite domain B∞ in the plane. We establish uniform approximation results in terms of the number of nodes on compact subsets of B∞ for solutions to nonhomogeneous hyperbolic partial differential equations in one of these spaces, (Formula presented.). 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.