1Problem Set #6 Power-flow solutions, Gauss-Seidel Method, and Newton-Raphson Method 6-1(Keyhani Lecture) Using Gauss elimination and back substitution, solve ⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡=⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡⎥⎥⎥⎦⎤⎢⎢⎢⎣⎡321142521240310321xxx6-2(Keyhani Lecture) Use Newton-Raphson to find one solution to the polynomial equation f(x)=y, where y=0 and f(x)=3x3+4x2+5x+6. Start with x(0)=1.0 and continue until ε<−−−)1()1()(ixixix(6.1) is satisfied, where ε=0.001. 6-3(Keyhani Lecture) Use Newton-Raphson to find a solution to ⎥⎦⎤⎢⎣⎡=⎥⎦⎤⎢⎣⎡+5.02.1)cos(2121xxexxwhere x1and x2are in radians. a)Start with x1(0)=1.0 and x2(0)=0.5 and continue until Equation (6.1) is satisfied with ε=0.005. b)Show that Newton-Raphson diverges for the example if x1(0)=1.0 and x2(0)=2.0. 6-4(Grainger and Stevenson, Jr. Chapter 8, Prob 8.10)
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