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一类非线性发展方程的特征中心差分法
Numerical Methods Based on Characteristic Centered Finite Difference Procedure for a Class of Nonlinear Evolution Equations
【摘要】 给出一类非线性发展方程的特征中心差分法,分别得到非规则网格上的位移u、速度ut及其对空间变量x的一阶导数项的差分解和误差估计.所讨论方法的计算量与基于线性插值的特征差分法相当,其近似解与基于二次插值的特征差分法的近似解具有相同阶的误差估计,u,ut对空间变量x的一阶导数近似均具有超收敛误差估计.数值试验说明了该方法的可行性和有效性.
【Abstract】 We propose a characteristic centered difference method for a class of nonlinear evolution equations on nonregular grids.Approximate solution and error estimate of u,ut,ux,utx are obtained.The compuational load of the method is the same as those of the characteristic difference method based on linear interpolation.And the error order of the approximate solution is the same as one of the characteristic difference method based on quadratic interpolation.Moreover,the first derivative of u,ut in space shows super-covergent order error estimate.Numerical results demonstrate feasibility and efficiency of the methods.
【Key words】 nonlinear evolution equation; characteristic centered finite difference method; error estimate;
- 【文献出处】 计算物理 ,Chinese Journal of Computational Physics , 编辑部邮箱 ,2007年06期
- 【分类号】O241.82
- 【被引频次】7
- 【下载频次】235