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Iterative Methods for Solving Non-Linear Equations

In: Numerical Methods for Grid Equations

Author

Listed:
  • Aleksandr A. Samarskii

    (Moscow University, Department of Computational, Mathematics and Cybernetics)

  • Evgenii S. Nikolaev

    (Moscow University, Department of Computational, Mathematics and Cybernetics)

Abstract

In this chapter we study iterative methods for solving non-linear difference schemes. In Section 13.1 we outline the general theory of iterative methods for abstract non-linear operator equations in a Hilbert space; various assumptions concerning the operators are considered. In Section 13.2, we look at the application of the general theory to the solution of difference analogs of boundary-value problems for quasi-linear second-order elliptic equations.

Suggested Citation

  • Aleksandr A. Samarskii & Evgenii S. Nikolaev, 1989. "Iterative Methods for Solving Non-Linear Equations," Springer Books, in: Numerical Methods for Grid Equations, chapter 0, pages 351-387, Springer.
    • Handle: RePEc:spr:sprchp:978-3-0348-9142-4_9
    DOI: 10.1007/978-3-0348-9142-4_9
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