一个施图姆-刘维尔方程最大特征值的逼近公式

An Approximation Formula of Sturm-liouville Equation′s Largest Eigenvalue

改进了一种计算施图姆-刘维尔方程大特征值的方法,运用泰勒展开对渐进公式中的奇异积分项进行近似,并且由于大特征值对应的特征函数具有较多零点这一特性,用系数在某点的取值来近似代替该周期的变化.对一类非常系数的施图姆-刘维尔方程的大特征值分布和逼近有较好的计算结果.考虑系数的变化,得到了一个改进的大特征值计算公式.算例表明,考虑扰动项的改进公式同样可以取得较好的计算结果.

A better method for computing the big eigenvalue approximation and distribution of a class of Sturm -liouville equation with variable coefficient is given. Improper-integral is approximated by using Taylor expansion formula in this method, and because the eigenfunction corresponding to big eigenvalue has many zero points,coefficient value in a point is used to approximate the replacement of the cycle. It shows better result of distribution and approximation of a class of variable coefficient Sturm - liouville equation＇s large eigenvalue. A better approximation result with an improved formula considering the incremental perturbation from the example is given.