Solving linear boundary value problems by approximating the coefficients

Author:
Steven A. Pruess

Journal:
Math. Comp. **27** (1973), 551-561

MSC:
Primary 65N15

DOI:
https://doi.org/10.1090/S0025-5718-1973-0371100-1

MathSciNet review:
0371100

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Abstract: A method for solving linear boundary value problems is described which consists of approximating the coefficients of the differential operator. Error estimates for the approximate solutions are established and improved results are given for the case of approximation by piecewise polynomial functions. For the latter approximations, the resulting problem can be solved by Taylor series techniques and several examples of this are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0371100-1

Keywords:
Linear boundary value problems,
piecewise polynomial approximation,
Richardson's extrapolation,
Taylor series methods,
shooting methods

Article copyright:
© Copyright 1973
American Mathematical Society