2Root Finding Methods for Nonlinear EquationsBisection MethodSecant MethodRegula-Falsi MethodNewton’s MethodMuller’s MethodFixed Point MethodNewton’s Method for Multiple RootsSystem of Non-linear EquationsNewton’s Methodand Fixed Point Method
3Introduction:In scientific and engineering studies, a frequently occurring problem is to find the roots or zeros of equations of the form f(x) =0.f(x)may be algebraicor transcendentalor a combination of both.Algebraic functions of the form P(x)= a0+ a1x + …+ anxn, are called polynomials.A non-algebraicfunction is called a transcendentalfunction.
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4Solution MethodsPolynomials up to degree 4 can be solved exactly.Since finding the root of f(x)=0is not always possible by analytical means, we have to go for some other techniques or methods.Solution Methods are eitherBracketing:Bisection Method, Regula Falsi Methodor Iterative:Secant Method, Newton's Method, Muller's Method, Fixed-Point Method.Rate of Convergence.Advantages/Disadvantages.