A difference spectral approximation based on the dimension reduction scheme for two-dimensional parabolic equations
For the second-order parabolic problem in a circular domain,we propose in this paper an ef-fective numerical method based on high-order polynomial approximation.The main idea of this method is to use polar coordinate transformation and Fourier basis function expansion to decompose the original problem into a series of decoupled one-dimensional second-order parabolic problems.Then,for each one-dimensional second-order parabolic problem,a weak form and its discrete scheme is established,and theoretically prove the stability of the schemes,the existence and uniqueness of the weak solution and the approximate solution,as well as the error estimate between them.Finally,some numerical exam-ples is presented,and the numerical results show the stability and convergence of our algorithm.
Second-order parabolic equationdifference spectral approximationstability and error esti-mationcircular domain
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