An Inversion Technique For The Laplace Transform With Application To Partial Differential Equation

The integro-differential equation of parabolic type often occurs in applications such as heat conduction in material with memory, compression of poro-viscoelastie media, population dynamics, nuclear reactor dynamics, etc.. There are lots of documents of V. Thomée [1,5,7,16,17,18,19,20,21,22,23,24,31], Stig. Larsson [19], W. Mclean[5,17,20,24], Ch. Lubich[18], J. C. López-Marcos[14], J. M. Sanz-Serna [6], G. Fairweather [3,15], L. Wahlbin[1,17,19], I. H. Sloan [7,18,22,23], Yanping Lin [31] in overseas and Chuan-miao Chen [1,35], Yun-qing Huang [2], Da Xu [8,9,10,11,12,13], Tao Tang [33], Qiya Hu [28], Tie Zhang [35] in home. A lot of them use FEM; Spline collocation methods; finite difference methods; Spectral collocation methods.We study a partial integro-differential equations of parabolic type with a weakly singular kernel.Main results follows:Given the numerical experiments and the full discretization for the linear equation of the lengendre spectral method in the direction of of x and the inversion technique for the laplace transform in the direction of t;(2)Given the numerical experiments and the full discretization for the linear equation of the Galerkin spectral method in the direction of of x and the inversion technique for the laplace transform in the direction of t;...