An accurate Chebyshev pseudospectral scheme for multi-dimensional parabolic problems with time delays
ملخص البحث
In this paper, the Chebyshev Gauss-Lobatto pseudospectral scheme is investigated in
spatial directions for solving one-dimensional, coupled, and two-dimensional
parabolic partial differential equations with time delays. For the one-dimensional
problem, the spatial integration is discretized by the Chebyshev pseudospectral
scheme with Gauss-Lobatto quadrature nodes to provide a delay system of ordinary
differential equations. The time integration of the reduced system in temporal
direction is implemented by the continuous Runge-Kutta scheme. In addition, the
present algorithm is extended to solve the coupled time delay parabolic equations.
We also develop an efficient numerical algorithm based on the Chebyshev
pseudospectral algorithm to obtain the two spatial variables in solving the
two-dimensional time delay parabolic equations. This algorithm possesses spectral
accuracy in the spatial directions. The obtained numerical results show the
effectiveness and highly accuracy of the present algorithms for solving
one-dimensional and two-dimensional partial differential equations.
الكلمات المفتاحيه
two-dimensional parabolic differential equations; delay system of differential equation; pseudospectral scheme; Chebyshev Gauss-Lobatto quadrature; continuous Runge-Kutta method