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The application of sparse matrix methods to the numerical solution of nonlinear elliptic partial differential equations

Part of the Lecture Notes in Mathematics book series (LNM,volume 430)

Abstract

We present a new algorithm for solving general semilinear, elliptic partial differential equations. The algorithm is based on Newton's Method but uses an approximate iterative method to solve the linear systems that arise at each step of Newton's Method. We show that the algorithm can maintain the quadratic convergence of Newton's Method and that it may be substantially faster than other available methods for semilinear or nonlinear partial differential equations.

This research was supported in part by the Office of Naval Research, N0014-67-A-0097-0016.

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© 1974 Springer-Verlag

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Eisenstat, S.C., Schultz, M.H., Sherman, A.H. (1974). The application of sparse matrix methods to the numerical solution of nonlinear elliptic partial differential equations. In: Colton, D.L., Gilbert, R.P. (eds) Constructive and Computational Methods for Differential and Integral Equations. Lecture Notes in Mathematics, vol 430. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0066268

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  • DOI: https://doi.org/10.1007/BFb0066268

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-07021-4

  • Online ISBN: 978-3-540-37302-5

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