一种径向基函数插值的ENO格式  

ENO scheme based on interpolation of radial basis function

作　　者：刘丽[1] 赵凤群[1] 

机构地区：[1]西安理工大学理学院,西安710054

出　　处：《计算机工程与应用》2013年第2期53-56,共4页Computer Engineering and Applications

基　　金：陕西省教育厅基金项目(No.11JK0524);陕西省自然科学基金(No.2011JM1013)

摘　　要：将ENO格式和径向基函数插值相结合,提出了求解双曲型偏微分方程的径向基函数插值的ENO方法。该方法依据ENO思想建立自适应模板,在选定的模板上利用径向基函数进行逼近,能够很好地处理具有间断解的问题,消除间断点处数值振荡现象。以一维双曲型偏微分方程为例,对该方法进行了验证,并通过与多项式ENO格式比较,表明该方法更具有优势。Combining the ENO scheme with radial basis function interpolation, an ENO method for solving hyperbolic partial di- fferential equations is introduced. According to the idea of ENO, the self-adjusting template is established, and the RBF interpola- tion is used to approximate in the selected template. Moreover, the problem with uncontinuous solution can be solved primely, and the numerical oscillation phenomenon at uncontinuous points is eliminated. Numerical results are presented for one-dimensional hyperbolic partial differential equation, and as compared with polynomial ENO method, this algorithm has more advantages.

关 键 词：守恒律方程 总变差减小(TVD) 基本无振荡(ENO)方法 径向基函数 

分 类 号：O242[理学—计算数学]