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A modification of Newton's method to solve the Dirichlet problem for the equation Δu=f(x, u)

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Abstract

The Dirichlet problem for a weakly nonlinear equation Δu=f(x, u) is investigated. We use successive approximations constructed by modified Newton's scheme and apply the extremal properties of the solutions of the elliptic equation of the form Δu − c(x)u=F(x), where c(x) ≥ 0. Numerical solution of the resulting sequence of linear boundary-value problems is considered.

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Literature cited

  1. A. V. Bitsadze, Boundary-Value Problems for Elliptic Equations of Second Order [in Russian], Nauka, Moscow (1966).

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Authors and Affiliations

  1. Kiev University, USSR

    Yu. A. Belov & V. F. Zrazhevskaya

Authors
  1. Yu. A. Belov
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  2. V. F. Zrazhevskaya
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Translated from Vychislitel'naya i Prikladnaya Matematika, No. 61, pp. 27–30, 1987.

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Belov, Y.A., Zrazhevskaya, V.F. A modification of Newton's method to solve the Dirichlet problem for the equation Δu=f(x, u). J Math Sci 63, 424–426 (1993). https://doi.org/10.1007/BF01849523

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  • DOI: https://doi.org/10.1007/BF01849523

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