奇异问题中奇异积分的数值方法

在许多实际问题中,需要数值计算奇异积分数值求解奇异微分方程的初、边值问题及奇异积分方程。提出的数值方法,处理了一些具有奇异被积函数的特殊函数,等离子体色散函数,第一类椭圆积分等。文中还导出了利用普通求积法计算各种奇异类型被积函数的求积公式,改善了用普通求积法计算不收敛或计算结果差的状况,特别是对多重积分计算更为显著。     

托卡马克位形求解的网格精细化

先进的托卡马克位形对于实现磁约束受控聚变是至关重要的。但对某些情况,精确计算位形是十分困难的。如当物理量在局部区域内有很大的变化,或在区域内解的数值大小有大的数量级上的改变,为保证数值求解平衡方程的收敛性,有两个困难随之产生了:(1)所需的计算机内存极大地增加,以致有的物理模式的计算受到计算机内存的限制。(2)求解代数方程阶次的迅速增长,可能使舍入误差的积累造成对真解的扭曲。利用两种     

MHD Flow Layer Formation at Boundaries of Magnetic Islands in Tokamak Plasmas

Non-linear development of double tearing modes induced by electron viscosity is numerically simulated. MHD flow layers are demonstrated to merge in the development of the modes. The sheared flows are shown to lie just at the boundaries of the magnetic islands, and to have suffcient levels required for internal transport barrier （ITB） formation. Possible correlation between the layer formation and triggering of experimentally observed ITBs, preferentially formed in proximities of rational flux surfaces of low safety factors, is discussed.     

多重积分数值方法研究

对多重积分数值计算的研究现状(包括理论、算法、程序)进行了综合评述,通过大量例子的数值计算对他们作了比较和讨论。提出了一种处理奇异被积函数积分的数值方法,成功地计算了其它方法不能计算的奇异积分。此外还介绍了在微机上移植、修改、建立的7个不同方法的计算多重积分的程序。     

Effects of m=0 Harmonics on Quasi-Linear Stage of m=1 Double Tearing Mode

Effects of tearing modes are inves shows that the effect of the m = 0 harmonics on the early quasi-linear stage of m = 1 double tigated. The numerical calculation with the harmonics m = 0 included the m = 0 harmonics on the mode is negligible in the linear stage. As the mode begins to grow nonlinearly, both the current and flow profiles are pinched due to the m = 0 harmonics. To make a comparison we also carry out the calculation with m = 0 harmonics turned off. The profiles of the total current, poloidal magnetic field, and poloidal shear velocity in the cases with or without the m = 0 harmonics are compared and discussed. In addition, the formation of a poloidal velocity shear is found and its mechanism is investigated.     

用样条配置法解边值问题

常微分方程边值问题数值方法远不如初值问题的数值方法那样完善和成熟,初值问题有相应的适应性很强的程序包。不过,多年来边值问题的数值方法也有了多方面的进展,如打靶法、多重打靶法、初值法(不变嵌入法)、外延修正差分法等,其相应的代码也有所建立。我们这里要推荐的是配置法及其代码colloc,colloc是基于高斯结点的样条配置     

有奇异解的奇异微分方程的数值方法研究

有奇异解的奇异微分方程的数值方法研究牟宗泽，隋国芳，何启兵（核工业西南物理研究院）ＮＵＭＥＲＩＣＡＬＭＥＴＨＯＤＳＦＯＲＳＩＮＧＵＬＡＲＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＷＩＴＨＳＩＮＧＵＬＡＲＳＯＬＵＴＩＯＮ￥ＭｏｕＺｏｎｇｚｅ；ＳｕｉＧｕ...