A Petrov–Galerkin spectral method for the linearized time fractional KdV equation
In this work, we consider the numerical approximation of a linearized time fractional KdV
equation in a bounded domain. A fully discrete scheme combining a Petrov–Galerkin
spectral method for the spatial discretization and L 1-approximation for the Caputo temporal
derivative is proposed. Stability and convergence of the fully discrete scheme are
rigourously established. Numerical results are presented to confirm the theoretical results.
equation in a bounded domain. A fully discrete scheme combining a Petrov–Galerkin
spectral method for the spatial discretization and L 1-approximation for the Caputo temporal
derivative is proposed. Stability and convergence of the fully discrete scheme are
rigourously established. Numerical results are presented to confirm the theoretical results.
Abstract
In this work, we consider the numerical approximation of a linearized time fractional KdV equation in a bounded domain. A fully discrete scheme combining a Petrov–Galerkin spectral method for the spatial discretization and L1-approximation for the Caputo temporal derivative is proposed. Stability and convergence of the fully discrete scheme are rigourously established. Numerical results are presented to confirm the theoretical results.
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