Finite Volume Element Method Based On Quadratic B-Spline For KDV Equation

Finite volume element method is an effective tool for solving partial differential equations. Due to its flexibility, simple calculation, easy program and local conservation property, finite volume element method draws more and more researchers'attention and favor, In recent years, finite volume element method has been widely used in the numerical solution of partial differential equations such as parabolic equations, elliptic equations, hyperbolic equations and so on. This paper provides a numerical scheme for the KDV equation by using quadratic B-spline finite volume method. KDV equation: ut+euux+/iuxxx= 0, (x, t) E [a, b] x (0, T], u(x,0)= u$(x), x G [a, b]. KDV equation is a class of typical nonlinear equations, demonstrating a major rule of nonlinear diffusion waves. It describes a number of physical phenomena such as lossless propagation and wave propagation behavior during interactions.The physical background of the KDV equation and some prior knowledge are illustrated first. Then, a quadratic B-spline finite volume method and the Crank-Nicolson discretization are provided to obtain the discrete scheme for the KDV equation. The method not only maintains the local conservation of momentum but also has high computational efficiency. At last, some benchmark examples are examined to verify the effectiveness of the method.