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Invariant imbedding applied to homogeneous two-point boundary-value problems with a singularity of the first kind. (English) Zbl 0488.65034


MSC:

65L10 Numerical solution of boundary value problems involving ordinary differential equations
34B05 Linear boundary value problems for ordinary differential equations
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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
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