半线性抛物型积分—微分方程的谱方法
Spectral Method for Semilinear Parabolic Integrodifferential Equations
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摘要: 本文在讨论带有半线性记忆项抛物型方程半离散格式的基础上,构造了空间方向谱离散,时间方向后欧拉方法的全离散格式,并给出了误差估计。对于记忆项的数值积分,采用了梯形公式与矩形公式结合的方法,并估计了数值积分的影响。Abstract: Based on the discussion of the semi discretization of a parabolic equation with a semilinear memory term,an error estimate is derived for the fully discrete scheme with spectral method in space and the backward Euler method in time The trapezoidal rule is adopted.for the quadrature of the memory term and the quadrature error isestimated.
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Key words:
- parabolic integro differential equation /
- spectral method /
- back-ward Euler method /
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[1] Yanik.E.G.and G.Fairweather,Finite element method for parabolic and hyperbolic partial integro-differential equations,Nonlinear Anal.,12(1988),785-80. [2] Canuto.C.et al.Spectral Method in Fluid Drnamics.Springer-Verlag(1987). [3] Sloan.I.H.and V.Thomee.Time discretization of an integro-differential equation of parabolic type.SIAM J.Numer.Anal.23(1986),1052-1061. [4] Le Roux.M-N.and V.Thomee.Numerical solution of semilinear integro-differential equations of parabolic type with nonsmooth data,SIAM J.Numer..Anal.,26(1989).1219-1309. [5] Gottlieb.D.Numerical analysis of spectral method,CBMS-NSF,Regional Conference Series in Applied Meth.26(1977). -
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