Cheng-Yu Ku1,2,3, Weichung Yeih1,2
CMC-Computers, Materials & Continua, Vol.31, No.3, pp. 173-200, 2012, DOI:10.3970/cmc.2012.031.173
Abstract In this paper, a dynamical Newton-like method with the adaptive stepsize based on the construction of a scalar homotopy function to transform a vector function of non-linear algebraic equations (NAEs) into a time-dependent scalar function by introducing a fictitious time-like variable is proposed. With the introduction of the fictitious time-like function, we derived the adaptive stepsize using the dynamics of the residual vector. Based on the proposed dynamical Newton-like method, we can also derive the dynamical Newton method (DNM) and the dynamical Jacobian-inverse free method (DJIFM) with the transformation matrix as the inverse of the Jacobian and the identity matrix,… More >
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