Compact Finite Volume Scheme And Its Error Analysis For Fourth-Order Linear Equation

The fourth-order equations have important physical meanings,such as the bal-ance and vibration problems of the beams and plates and the growth of crystals,ect.so,the analysis of them numerical solution has certain application significance.In this paper,we following mainly study compact finite volume scheme for fourth-order linear equation.(1)One dimensional constant fourth-order linear equation(2)One dimensional parabolic equation Among them,f(x,t)about x?t properly smooth.(3)One dimensional constant fourth-order linear equations Among them,f(x,y)aboutx?y properly smooth.In order to construct the high precision numerical solution format for the above problems,we let the fourth-order equation is translated into a system of two secound-order equations by introducing a new variable.Then the compact finite volurme scheme is obtained for this system and the error analysis is proved.The numerical experiment shows this scheme has satisfying performance.