Abstract
The Laplace transform method has proven to be very efficient for dealing with parabolic problems whose coefficients are time independent, and it is easily parallelizable. However, the method has not been proven to be applicable to linear problems whose coefficients are time dependent. The reason is that the Laplace transform of two time-dependent functions leads to a convolution of the Laplace transformed functions in the dual variable. In this paper, we propose a Laplace transform method to linear parabolic problems with time-dependent coefficients, which is as efficient as the method for parabolic problems with time-independent coefficients. Several numerical results are provided, which support the efficiency of the proposed scheme.
Published Version
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