A Bellman's procedure for a phase change problem

Bellman, 1972, Differential Quadrature: A Thechnique for the rapid solution of non linear partial differential equations, J. Comp. Phys., 10, 52 Fasano, 1983 Fornberg, 1975, On a Fourier method for the integration of hyperbolic equations, SIAM J. Num. An., 12, 509, 10.1137/0712040 Kreiss, 1972, Comparison of accurate methods for the integration of hyperbolic equations, Tellus, 14, 199, 10.1111/j.2153-3490.1972.tb01547.x Özisik, 1980 Satofuka, 1983, A New Explicit Method for the Numerical Solution of Parabolic Differential Equations 1978