Methods for Solving Systems of Nonlinear Equations

Various methods derived from single equation solutions can be used to solve simultaneous nonlinear equations. This section extends the Newton-Raphson method to handle systems of n equations in n variables. The procedure involves concepts like matrices, vectors, norms, and solutions of linear systems. Starting with an initial estimate vector, the Newton-Raphson method seeks an improved estimate based on truncated Taylor series. The multivariable Newton-Raphson method follows steps outlined in Procedure 3.5. Numerical integration techniques like the Trapezoidal rule and Simpson’s rule are introduced for evaluating integrals of polynomials.

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