Characteristic Finite Volume Element Method For Generalized Nerve Conduction Equation

In this paper, through the idea of characteristic direction method and theory of finite volume element, two characteristic finte volume element methods are introduced and analyzed for approximating the solution of a nonlinear-hyperbolic eqation in 2-space variables. Piece-wise quadratic trial functions and piecewise constant test functions are used to finally obtain the convergence rate of two numerical schemes. In section 2, we give some notations and some lemmas. Section 3 of this thesis is to slove the problem in single-step characteristic finite volume element method, and a numerical experiment is given which showed the method is practical. Section 4 is to use multi-step characteristic finite volume element method to solve the problem, finally it is important that theoretical analysis as well as numerical results shows that compared to single-step method, multi-step method improve the accuracy.