KdV方程的二次B样条有限元孤立子模拟

Computer Simulation of KdV Equation Using Square B-spline Finite Element Method and Solition

应用Bubnov -Galerkin方法及二次B样条有限元方法 ,得到一种数值计算解KdV方程的方法。对其产生的五对角矩阵方程用数值线代数的Doolittle三角分解方法求解 ,并对这种格式的线性稳定性进行了分析研究。结合孤立子模型编写了该算法的计算机程序 ,从而得到了给定初边值条件下的KdV方程数值模拟结果。

By using Bubnov-Galerkin method and square B-spline finite element method, this paper discusses the numerical solution to KdV equation. The quintuple-diagonal matrix out of the equation is solved by way of linear algebraic Doolittle decomposition. The linear stability of this method is also studied. Based on the soliton model, an algorithm program in C++ language is completed to figure out the simulation result under given boundary conditions.