Abstract
At the present work, we propose a new numerical scheme for the solution of two and three dimensional time fractional nonlinear damped Klein–Gordon equation (DKGE). To this end, we use the Legendre spectral element method to discretize the equation in the spatial directions and for the time stepping, an alternating direction implicit (ADI) method based on a scheme of order O(τ2) is considered. We prove that the presented method is unconditionally stable and obtain an error estimate for the fully discrete scheme. The presented numerical experiments demonstrate the good accuracy and efficiency of the proposed ADI spectral element method.
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