54 if p q etc are the matrices introduced at the

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Unformatted text preview: ne the unknowns in z corresponding to \odd" numbered blocks in B by forward substitution using the lower triangular matrices L( ) , i = 0 1 : : : N . Knowing these unknowns, the remaining components of z may be determined by backward substitution using the \even" numbered blocks and the upper triangular matrices U( ) , i = N N ; 1 : : : 0. Slightly di erent procedures are given in Ascher et al. 1], Section 7.2 and Diaz et al. 4]. i i 24 Bibliography 1] U.M. Ascher, R. Mattheij, and R. Russell. Numerical Solution of Boundary Value Problems for Ordinary Di erential Equations. SIAM, Philadelphia, second edition, 1995. 2] J.M. Coyle, J.E. Flaherty, and R. Ludwig. On the stability of mesh equidistribution strategies for time-dependent partial di erential equations. Journal of Computational Physics, 62:26{39, 1986. 3] C. de Boor. A Practical Guide to Splines. Springer-Verlag, New York, 1978. 4] J.C. Diaz, G. Fairweather, and P. Keast. Fortran packages for solving almost block diagonal linear systems by modi ed alternate row and column elimination. ACM Transactions on Mathematical Software, 9:358{375, 1981. 5] E. Isaacson and H.B. Keller. Analysis of Numerical Methods. John Wiley and Sons, New York, 1966. 6] H.B. Keller. Accurate di erence methods for linear ordinary di erential systems subject to linear constraints. SIAM J. Numer. Anal., 6:8{30, 1969. 7] M. Lentini and V. Pereyra. An adaptive nite di erence solver for nonlinear two point problems with mild boundary layers. SIAM J. Numer. Anal., 14:91{111, 1977. 8] J.M. Varah. Alternate row and column elimination for solving certain linear systems. SIAM J. Numer. Anal., 13:71{75, 1976. 25...
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