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Comput."],"published-print":{"date-parts":[[2024,6]]},"abstract":"<jats:p> A second-order time-stepping method for numerically solving the linearized time fractional KdV equation (TFKDVE) whose solution has initial singularity is investigated. Alikhanov\u2019s scheme is used to discretize the Caputo fractional derivative on temporal graded mesh, and the space is approximated by a Petrov\u2013Galerkin spectral method. Detailed stability and error estimate of the full-discrete scheme are given, and the final error bound is [Formula: see text]-robust. 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