Abstract
Recent developments in the area of nonlinear differential boundary value problems include two general techniques that involve grid manipulation, namely, deterministic mesh refinement and multigrid methods. They can be combined very effectively to produce a safe, efficient algorithm for many classes of problems. The object of this paper is to consider the application of those methods to the solution of nonlinear integral equations including eigenproblems for integral operators. This paper will also include a report on some numerical experiments with these methods.
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References
E.L. Allgower, S.F. McCormick, and D.V. Pryor, “A general mesh independent principle for Newton’s method applied to second-order boundary value problems”, J. Numer. Funct. Anal.Opt., to appear.
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S.F. McCormick, “A revised mesh refinement strategy for numerical solution of two-point boundary value problems”, Springer 679, Berlin (1978), 15–23.
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McCormick, S. (1980). Mesh Refinement Methods for Integral Equations. In: Albrecht, J., Collatz, L. (eds) Numerical Treatment of Integral Equations / Numerische Behandlung von Integralgleichungen. International Series of Numerical Mathematics / International Schriftenreihe zur Numerischen Mathematik / Série internationale d’Analyse numérique, vol 53. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-6314-8_13
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DOI: https://doi.org/10.1007/978-3-0348-6314-8_13
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-7643-1105-6
Online ISBN: 978-3-0348-6314-8
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