A GPGPU based program to solve the TDSE in intense laser fields through the finite difference approach. We present a General-purpose computing on graphics processing units (GPGPU) based computational program and framework for the electronic dynamics of atomic systems under intense laser fields. We present our results using the case of hydrogen, however the code is trivially extensible to tackle problems within the single-active electron (SAE) approximation. Building on our previous work, we introduce the first available GPGPU based implementation of the Taylor, Runge-Kutta and Lanczos based methods created with strong field ab-initio simulations specifically in mind; CLTDSE. The code makes use of finite difference methods and the OpenCL framework for GPU acceleration. The specific example system used is the classic test system; Hydrogen. After introducing the standard theory, and specific quantities which are calculated, the code, including installation and usage, is discussed in-depth. This is followed by some examples and a short benchmark between an 8 hardware thread (i.e. logical core) Intel Xeon CPU and an AMD 6970 GPU, where the parallel algorithm runs 10 times faster on the GPU than the CPU.