Nelson, Paul; Sagong, Seok; Elder, Ira T. Invariant imbedding applied to homogeneous two-point boundary-value problems with a singularity of the first kind. (English) Zbl 0488.65034 Appl. Math. Comput. 9, 93-110 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 4 Documents MSC: 65L10 Numerical solution of boundary value problems involving ordinary differential equations 34B05 Linear boundary value problems for ordinary differential equations Keywords:invariant imbedding; homogeneous differential systems; singularity of the first kind; second-order equation; numerical examples Citations:Zbl 0271.34001; Zbl 0486.65054 PDFBibTeX XMLCite \textit{P. Nelson} et al., Appl. Math. Comput. 9, 93--110 (1981; Zbl 0488.65034) Full Text: DOI References: [1] Scott, M. R., Invariant Imbedding and its Applications to Ordinary Differential Equations (1973), Addison-Wesley: Addison-Wesley Reading, Mass [2] Casti, J. L.; Kalaba, R. E., Imbedding Methods in Applied Mathematics (1973), Addison-Wesley: Addison-Wesley Reading, Mass · Zbl 0265.65001 [3] Bellman, R. E.; Wing, G. M., An Introduction to Invariant Imbedding (1975), Wiley: Wiley New York · Zbl 0325.34001 [4] Banks, D. O.; Kurowski, G. J., Computation of eigenvalues of singular Sturm-Liouville systems, Math. Comp., 22, 304-310 (1968) · Zbl 0187.11301 [5] I.T. Elder, An invariant imbedding method for computation of eigenlengths of singular two-point boundary-value problems, J. Math. Anal. Appl., to appear.; I.T. Elder, An invariant imbedding method for computation of eigenlengths of singular two-point boundary-value problems, J. Math. Anal. Appl., to appear. · Zbl 0486.65054 [6] Boland, W. R.; Nelson, P., Critical lengths by numerical integration of the associated Riccati equation to singularity, Appl. Math. Comput., 1, 67-82 (1975) · Zbl 0334.65064 [7] Nelson, P.; Elder, I. T., Calculation of eigenfunctions in the context of integration-to-blowup, SIAM J. Numer. Anal., 14, 124-136 (1977) · Zbl 0357.65060 [8] Scott, M. R.; Vandevender, W. H., A comparison of several invariant imbedding algorithms for the solution of two-point boundary-value Problems, Appl. Math. Comput., 1, 187-218 (1975) · Zbl 0335.65031 [9] Scott, M. R., Invariant imbedding and the calculation of internal values, J. Math. Anal. Appl., 28, 112-119 (1969) · Zbl 0186.41202 [10] Nelson, P.; Scott, M. R., Internal values in particle transport by the method of invariant imbedding, J. Math. Anal. Appl., 34, 628-643 (1971) · Zbl 0217.53002 [11] Coddington, E. A.; Levinson, N., Theory of Ordinary Differential Equations (1955), McGraw-Hill: McGraw-Hill New York · Zbl 0042.32602 [12] DeHoog, F. R.; Weiss, R., Difference methods for boundary value problems with a singularity of the first kind, SIAM J. Numer. Anal., 13, 775-813 (1976) · Zbl 0372.65034 [13] Shampine, L. R.; Allen, R. C., Numerical Computing (1973), Saunders: Saunders Philadelphia This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.