Gray-Scott模型的高階緊致線性化差分格式

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Abstract：The Gray-Scott equation of integer order with Dirichlet boundary condition is studied. We propose a numerical scheme for solving eficiently the Gray-Scottequation by combining the compact diffrence method and the operator splitting algorithm. Firstly，the original problem is decomposed into linear and nonlinear parts based on the operator spliting idea. Then the linear subproblem is solved by using the fourth-order compact difference scheme，the nonlinear subproblem is solved by using the Crank-Nicolson diference scheme，and the nonlinear terms are handled by using the Rubin-Graves linearization technique to build a linear solving format to achieve an eficient solution.Finally，the stability of the scheme is proved，the error estimate of given，and the validity of the scheme is verified by numerical experiments.

Keywords：：Gray-Scott equation；operator spliting；fourth-order compact difference scheme；Rubin-Graves linearization technique；stability；validity

Gray-Scott（GS）模型是一種用于描述反應(yīng)-擴(kuò)散的數(shù)學(xué)模型，該模型最初由物理學(xué)家Gray 和 Scott在 1984 年提出[1]，廣泛用于研究自然界和工業(yè)過程中的模式形成和結(jié)構(gòu)動力學(xué)[2-9]，主要關(guān)注兩種化學(xué)物質(zhì)之間的反應(yīng)和擴(kuò)散過程。（剩余8304字）