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This paper presents the development of a two-dimensional (2-D) finite-difference time-domain (FDTD) solver that features reliable calculations and reduced simulation times. The accuracy of computations is guaranteed by specially-designed spatial operators with extended stencils, which are assisted by an optimized version of a high-order leapfrog integrator. Both discretization schemes rely on error-minimization concepts, and a proper least-squares treatment facilitates further control in a wideband sense. Given the parallelization capabilities of explicit FDTD algorithms, considerable speedup compared to serialized CPU calculations is accomplished by implementing the proposed algorithm on a modern graphics processing unit (GPU). As our study shows, the GPU version of our technique reduces computing times by several times, thus confirming its designation as a highly-efficient algorithm.