An Efficient Iterative Approach to Large Sparse Nonlinear Systems with Non-Hermitian Jacobian Matrices

Abstract

Inner-outer iterative methods for large sparse non-Hermitian nonlinear systems are considered. Using the ideas of modified generalised Hermitian and skew Hermitian methods and double-parameter GHSS method, we develop a double-parameter modified generalised Hermitian and skew Hermitian method (DMGHSS) for linear non-Hermitian systems. Using this method as the inner iterations and the modified Newton method as the outer iterations, we introduce modified Newton-DMGHSS methods for large sparse non-Hermitian nonlinear systems. The convergence of the methods is studied. Numerical results demonstrate the efficacy of the methods.