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Iterative Methods for Solving Non-Linear Equations

A. A. Samarskiĭ, Evgenii S. Nikolaev

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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.

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What this paper is about

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.

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Available 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.

Key concepts: Mathematics, Iterative method, Hilbert space, Applied mathematics, Boundary value problem, Section (typography), Linear equation, Linear system

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