Minimax approximate solutions of linear boundary value problems

Authors:
Darrell Schmidt and Kenneth L. Wiggins

Journal:
Math. Comp. **33** (1979), 139-148

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514815-X

MathSciNet review:
514815

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Abstract: Define the operator by where and consider the two point boundary value problem , , , where , and . Let denote the set of polynomials of degree at most *k* and define the approximating set . Then for each there exists satisfying , where denotes the uniform norm on . If the homogeneous BVP , has no nontrivial solutions, then the nonhomogeneous BVP has a unique solution *y* and for . If *X* denotes a closed subset of and

*X*in . Several numerical examples are given.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1979-0514815-X

Keywords:
Minimax approximate solution,
uniform approximation,
boundary value problem

Article copyright:
© Copyright 1979
American Mathematical Society