The linearized Vlasov and Poisson equations governing electron plasma oscillations are solved numerically for the case of a Maxwellian electron gas confined by a linear potential. An iterative method of solving the wave equation is developed using a local Fourier transform to demonstrate convergence of the method. The numerical solution verifies and extends the results obtained analytically with the WKB theory by Berk, Horton, Rosenbluth, and Sudan. The reflection coefficient obtained from the numerical solution is compared with the first‐order WKB reflection coefficient. The numerical calculation demonstrates that the higher‐order reflection processes are smaller than the first‐order process.