The difference in computational power between the few- and multicore architectures represented by central processing units (CPUs) and graphics processing units (GPUs) is significant today, and this difference is likely to increase in the years ahead. GPUs are, therefore, ever more popular for applications in computational physics, such as wave modeling. Finite-difference methods are popular for wave modeling and are well suited for the GPU architecture, but developing an efficient and capable GPU implementation is hindered by the limited size of the GPU memory. I revealed how the out-of-core technique can be used to circumvent the memory limit on the GPU, increasing the available memory to that of the CPU (the main memory) instead, with no significant computational overhead. This approach has several advantages over a parallel scheme in terms of applicability, flexibility, and hardware requirements. Choices in the numerical scheme — the numerical differentiators in particular — also greatly affect computational efficiency. These factors are considered explicitly for GPU implementations of wave modeling because GPUs are special purpose with a visible architecture.