Two Numerical Methods For Sobolev Equation

The Sobolev equation is a kind of equation widely used in fluid dynamics and thermo-dynamics, due to its physical significance, many experts and scholars pay close attentionto it. In this paper, we use block-centered finite diference method and the characteris-tics of block-centered finite diference method to solve two kinds of linear equations of theSobolev initial boundary value problem,respectively. We get the approximate solution andthe approximate solution of the first order derivative of the solutions, and we can obtainthe approximate solution of the first order derivative of the solutions is super convergence.First of all, there is an overview of the background and development status of equationand the method to solve the equation, in addition, simply introduced the work we do andthe basic theory of knowledge involved in this paper.Moreover, for the general linear Sobolev equation with initial boundary value problem,by introducing a derivative variable, we structure the block centered diference format inan isometric mesh, and do its error estimation, the corresponding numerical examples aregiven; for the initial boundary value problem of Sobolev equation with convection andconvection dominated, to maintain the important physical properties of the equation, wecombinate the characteristic line and the block-centered diference methods to constructcharacteristics of block-centered finite diference format, analyse and prove the convergenceand stability. In the end, a numerical example is provided to show the correctness of thetheoretical analysis. Finally, the summary and the development prospects of equation are given.