Numerical Ealculation Of A Kind Of Partial Integral Differential Equation

The integro-differential equation of parabolic type oftenoccurs in application such as heat conduction in material withmemory, comression of poro-viscoelastic media, nuclear reactordynamics,ect. theres are lots of documents of V. thomee ([1,2,8,11,12,14]),W. Mclean ([2,8,14]), Ch. Lubich ([15,16]),L. Wahlbin([1]),Sanz-Serna([3]), E.G. Yanik, G. Fairwea-ther ([5]) in overseas and Chuan-miao Chen ([1]),Yuan-qingHuang ([10]),Da-Xu ([17,18]) in home. A lot of them useFEM;Spectral collocation methods;Spline collocation methods.but few of them use six-point implicit scheme,numericalinversion for the laplace transform,umerical inversion forthe laplace transform of Lubich.We study a partial integro-differential equations of para-bolic type with a weakly singular kernel, which use six-pointimplicit scheme and numerical inversion for the laplace tran-sform fully discrete in time and space for numerical calcul-ation, main results follows:(1) Give a kind of fully discrete scheme of a partialintegro-differential equations which use six-point implicitscheme in the direction of space x and numerical inversion forthe laplace transform in the direction of time t for numericalcalculation.(2) Give a kind of fully discrete scheme of a partialintegro-differential equations which use six-point implicitscheme in the direction of space x and numerical inversion forthe laplace transform of Lubich in the direction of time t for numerical calculation.(3) Give a kind of fully discrete scheme for constantdifferential equations which use numerical inversion for thelaplace transform of Lubich for numerical calculation.Calculating result of some methods is accuratly higher,and calculate is simpler also.