Numerical differentiation of implicitly defined space curves

摘要: In this note we develop a simple finite differencing device to calculate approximations of derivativesx′(0),x″(0),x (3)(0), … regular solution curvesx: ℜ ∋s →x(s) ∈ ℜ n nonlinear systems equationsg(x)=0,g∈C k (ℜ n + 1, ) without having compute points on the arcx(s). The derivative vectorsx′(0),x″(0),x (3)(0),… can be used in numerical approximation setg −1(0) two ways. On one hand they applied construct higher order predictors predictor-corrector branch following procedures. other serve as determining basis functions Reduced Basis Method. performance method is demonstrated by some examples.