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nonlinear systems; inexact Newton-like methods; composite iterations; deformation theory of plasticity; numerical experiments; nonlinear elliptic problems; generalized Picard method; secant modulus method; preconditioned conjugate gradients; convergence
Newton-like methods are considered with inexact correction computed by some inner iterative method. Composite iterative methods of this type are applied to the solution of nonlinear systems arising from the solution of nonlinear elliptic boundary value problems. Two main quastions are studied in this paper: the convergence of the inexact Newton-like methods and the efficient control of accuracy in computation of the inexact correction. Numerical experiments show the efficiency of the suggested composite iterative techniques when problems of the deformation theory of plasticity are solved.
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