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Winter 1999 Solving Boundary Value Problems Numerically Using Steepest Descent In Sobolev Spaces
W. T. Mahavier
Missouri J. Math. Sci. 11(1): 19-32 (Winter 1999). DOI: 10.35834/1999/1101019


Elementary boundary value problems are used as a vehicle to introduce upper level undergraduate students or first year graduate students to descent algorithms. The paper is expository in nature and includes references for Euclidean and Sobolev steepest descent while serving as an introduction to optimization techniques such as variable metric and conjugate gradient methods. Numerical algorithms for solving boundary value problems with both Euclidean and Sobolev descent are developed. Results for constrained, unconstrained, and singular problems are displayed and properties of descent algorithms are outlined.


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W. T. Mahavier. "Solving Boundary Value Problems Numerically Using Steepest Descent In Sobolev Spaces." Missouri J. Math. Sci. 11 (1) 19 - 32, Winter 1999.


Published: Winter 1999
First available in Project Euclid: 23 November 2019

zbMATH: 1097.65535
MathSciNet: MR1674522
Digital Object Identifier: 10.35834/1999/1101019

Rights: Copyright © 1999 Central Missouri State University, Department of Mathematics and Computer Science


Vol.11 • No. 1 • Winter 1999
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