Computing the indices of Sturm–Liouville eigenvalues for coupled boundary conditions (the EIGENIND-SLP codes) |
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| Authors: | Guixia Wang Zhong Wang Hongyou Wu |
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| Institution: | aDepartment of Mathematics, Inner Mongolia University, Hohhot 010021, China;bDepartment of Mathematics, Inner Mongolia Normal University, Hohhot 010022, China;cDepartment of Mathematics, ZhaoQing University, GuangDong 526061, China;dDepartment of Mathematics, Northern Illinois University, DeKalb, IL 60115, USA |
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| Abstract: | The main purpose of the EIGENIND-SLP codes is to compute the indices of known eigenvalues of self-adjoint Sturm–Liouville problems with coupled boundary conditions (BCs). The spectrum of the problems can be unbounded from both below and above. Using some recent theoretical results, the computation is converted to that of the indices of the same eigenvalues for appropriate separated BCs, and is then carried out in terms of the Prüfer angle. The algorithm so generated and its implementation are discussed, and numerous examples are presented to illustrate the theoretical results and various aspects of the implementation. |
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| Keywords: | Self-adjoint Sturm– Liouville problems Indices of eigenvalues Coupled boundary conditions Prü fer angle Numerical computations |
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