| In this paper, we study two questions. The first is the integro-differential equation of parabolic type often occurs in applications such as heat conduction in material with memory, compression of poro-viscoelastic 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 [34], Tie Zhang [38] in home. A lot of them use FEM; Spline collocation methods; finite difference methods; Spectral collocation methods. But few of them make the linear equation of the linear finite element method in the direction of of x and the inversion technique for the laplace transform in the direction of t. The second is the quasilinear equation of elliptic type in application such as infiltrates surface of heap leaching process. All are interested in building mathematical models of different types of heap leaching rates and parameters. It is particularly important and urgent to describe particularly in mathematicacs. The artical presents the difference method first to obtain the discretization, and then applies single rank inverse Broyden iterative method and newton iterative method.Mam results follows:(1)Given the numerical experiments and the full discretization for the linear equation of the linear finite element 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 Single Rank Inverse Broyden Iterative method for a Nonlinear Problems to Infiltrates Surface of Heap Leaching Process.(3)Given the numerical experiments and Newton Iterative method for a Nonlinear Problems to Infiltrates Surface of Heap Leaching Process.
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