Latent heat thermal energy storage (LHTES) problems include a lot of boundary conditions that could not be solved by exact solution, so new approaches to solving such problems could revolutionize the advanced energy storage devices. This paper focuses on reformulating the generalized differential quadrature method (GDQM) for a one-dimensional solidification/melting Stefan problem as a fundamental LHTES problem and solves some practical cases. Convergence and comparisons demonstrate that the proposed approach is sufficiently reliable. By checking the accuracy of the proposed approach for the LHTES problem (where Stefan number is below 0.2), it was demonstrated that for all Stefan numbers, the maximum error is less than 3.81% for temperatures. As the usual range of thermal energy storages, for Stefan numbers up to 0.2 the solution yields errors less than 0.2%. Then, the proposed approach is very ideal for such applications. In comparison, GDQM has a more accurate response than an integral solution for Stefan numbers less than 0.2. When this priority of GDQM comes with its low computational cost, it would undoubtedly be preferable.