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Abstract
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In this work, we propose a numerical technique based on the Padé scheme for solving the two-sided space-fractional diffusion equation. First, space fractional diffusion equations are approximated with respect to space variable. We will achieve a system
of ODE. Then by applying a parallel implementation of the A-stable methods, this system is solved. Also, we use of the presented method for pricing European call option under a geometric Lévy process. Illustrative examples are included to show the accuracy and applicability of the new technique presented in the current paper.
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