کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
4639647 | 1341242 | 2012 | 14 صفحه PDF | دانلود رایگان |
For the generalized Sturm–Liouville problems we can construct an SL(2,R)SL(2,R) Lie-group shooting method to find eigenvalues. By using the closure property of the Lie-group, a one-step Lie-group transformation between the boundary values at two ends of the considered interval is established. Hence, we can theoretically derive an analytical characteristic equation to determine the eigenvalues for the generalized Sturm–Liouville problems. Because the closed-form formulas are derived to calculate the unknown left-boundary values in terms of λλ, the present method provides an easy numerical implementation and has a cheap computational cost. Numerical examples are examined to show that the present SL(2,R)SL(2,R) Lie-group shooting method is effective.
Journal: Journal of Computational and Applied Mathematics - Volume 236, Issue 17, November 2012, Pages 4547–4560