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Accurate simulation of oscillating edge flames is computationally very challenging because of the difficult calculations involved to incorporate most of the physics that is believed to be central to the phenomenon. This paper presents the design of a new simulation tool that can handle among other things the concept of flame speed. The conditions for the existence of unique solutions of energy and species equations are established by the actual solution method and the Lipschitz continuity approach. The analytical solution is obtained via Olayiwola’s generalized polynomial approximation method (OGPAM), which shows the influence of the parameters involved on the system. Both the effects of an on-edge and offedge convective flow, and the effects of a heat sink were examined. The effect of changes in values of parameters such as the Damkohler number and speed with which the flame advances are presented graphically and discussed.