Abstract
Procedures for the solution of nonlinear algebraic, discrete equations arising from the application of the finite element method to initial-boundary value problems in structural mechanics are described and evaluated. Properties of Newton's method, modified Newton method and quasi-Newton including asymptotic cost estimates and local convergence characteristics, are discussed. The use of Lanczos algorithm to solve the linearized set of equations arising at each iterate of Newton's method, is investigated. The result is a technique whereby the rate of convergence can be varied from superlinear to quadratic by controlling a certain tolerance. The above methods are compared on several quite different nonlinear problems in structural mechanics and the results are encouraging.
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