Cheng-Yu Ku1
CMES-Computer Modeling in Engineering & Sciences, Vol.96, No.6, pp. 409-434, 2013, DOI:10.3970/cmes.2013.096.409
Abstract This paper proposes a novel method, named the dynamical Jacobianinverse free method (DJIFM), with the incorporation of a two-sided equilibrium algorithm for solving ill-conditioned systems of linear equations with extreme physical property contrasts. The DJIFM is based on the construction of a scalar homotopy function for transforming the vector function of linear or nonlinear algebraic equations into a time-dependent scalar function by introducing a fictitious time-like variable. The DJIFM demonstrated great numerical stability for solving linear or nonlinear algebraic equations, particularly for systems involving ill-conditioned Jacobian or poor initial values that cause convergence problems. With the incorporation of a newly… More >
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