Galerkin methods for singular boundary value problems in one space dimension

Authors:
Kenneth Eriksson and Vidar Thomée

Journal:
Math. Comp. **42** (1984), 345-367

MSC:
Primary 65L60; Secondary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736441-1

MathSciNet review:
736441

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Abstract | References | Similar Articles | Additional Information

Abstract: Two Galerkin type piecewise polynomial approximation procedures based on bilinear forms with different weight functions are analyzed and compared. Optimal order error estimates are proved and numerical results are presented.

**[1]**D. C. Brabston & H. B. Keller, "A numerical method for singular two-point boundary value problems,"*SIAM J. Numer. Anal.*, v. 14, 1977, pp. 779-791. MR**0483475 (58:3476)****[2]**F. R. de Hoog & R. Weiss, "On the boundary value problem for systems of ordinary differential equations with a singularity of the second kind,"*SIAM J. Numer. Anal.*, v. 11, 1980, pp. 41-60. MR**556495 (81a:34017)****[3]**S. G. Eisenstat, R. S. Schreiber & M. H. Schultz,*Finite Element Methods for Spherically Symmetric Elliptic Equations*, Yale Computer Science Report No. 109, 1977.**[4]**B. Gustafsson, "A numerical method for solving singular boundary value problems,"*Numer. Math.*, v. 21, 1973, pp. 328-344. MR**0337015 (49:1788)****[5]**P. Jamet, "On the convergence of finite-difference approximations to one-dimensional singular boundary-value problems,"*Numer. Math.*, v. 14, 1970, pp. 355-378. MR**0261799 (41:6411)****[6]**D. Jespersen, "Ritz-Galerkin methods for singular boundary value problems,"*SIAM J. Numer. Anal.*, v. 15, 1978, pp. 813-834. MR**0488786 (58:8296)****[7]**R. D. Russel & L. F. Shampine, "Numerical methods for singular boundary value problems,"*SIAM J. Numer. Anal.*, v. 12, 1975, pp. 13-36. MR**0400723 (53:4553)****[8]**R. Schreiber & S. C. Eisenstat, "Finite element methods for spherically symmetric elliptic equations,"*SIAM J. Numer. Anal.*, v. 18, 1981, pp. 546-558. MR**615530 (82f:65118)****[9]**M. F. Wheeler, " estimates of optimal orders for Galerkin methods for one-dimensional second order parabolic and hyperbolic equations,"*SIAM J. Numer. Anal.*, v. 10, 1973, pp. 908-913. MR**0343658 (49:8398)**

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1984-0736441-1

Keywords:
Singular two-point boundary value problem,
singular parabolic equation,
spherical symmetry,
piecewise polynomial approximation,
Galerkin's method,
error estimate

Article copyright:
© Copyright 1984
American Mathematical Society