Chein-Shan Liu^{1,2}, Hong-Hua Dai^{1}, Satya N. Atluri^{1}

*CMES-Computer Modeling in Engineering & Sciences*, Vol.81, No.2, pp. 195-228, 2011, DOI:10.3970/cmes.2011.081.195

Abstract In this continuation of a series of our earlier papers, we define a hyper-surface *h*(x,*t*) = 0 in terms of the unknown vector x, and a monotonically increasing function *Q(t)* of a time-like variable t, to solve a system of nonlinear algebraic equations **F(x)** = **0**. If **R** is a vector related to ∂h / ∂x, , we consider the evolution equation **x**^{·} = λ[αR + βP], where **P = F − R(F·R) / ||R||**^{2} such that **P·R** = 0; or **x**^{·} = λ[αF + βP^{∗}], where **P**^{∗} = R − F(F·R) / ||F||^{2} such that **P**^{*}·F =… More >