i) By making use of Taylor Series expansions derive the form of the two dimensional Newton-Rhapson Iteration process, suitable for obtaining a solution to
\(\displaystyle f(x,y)\ =\ 0,\)
\(\displaystyle g(x,y)\ =\ 0.\)
ii) By first calculating \(\displaystyle \Delta^k(e^{\alpha x_j})\) for equally spaced \(\displaystyle x_j\) calculate \(\displaystyle \Delta^{k}x^k_j\) for fixed \(\displaystyle k\).
Thank you for any help.
\(\displaystyle f(x,y)\ =\ 0,\)
\(\displaystyle g(x,y)\ =\ 0.\)
ii) By first calculating \(\displaystyle \Delta^k(e^{\alpha x_j})\) for equally spaced \(\displaystyle x_j\) calculate \(\displaystyle \Delta^{k}x^k_j\) for fixed \(\displaystyle k\).
Thank you for any help.
