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   Skip Navigation LinksHOME › AREAS OF EXPERTISE › Nonlinear Systems Applications › ~ Fixed Point / Birge-Vieta Methods


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FIXED POINT METHOD
Fixed Point



The idea behind the fixed point method is very simple: to find the solutions of a given nonlinear function f(x) = 0, it is possible to rearrange f(x)= 0 into the form x = g(x), where g(x) denotes a function of x. Then, simply start with an initial guess, x0 and apply the iteration process:

xn = g(xn - 1)     for n = 1,2,3,...

For example, to find solutions for the following nonlinear equation:

f(x) = sin x + ex + x2 - 2x = 0

There are several ways to rewrite the above equation into the form x = g(x). For example, it is possible to rearrange the above equation into the following form:

x = 1/2(sin x + ex + x2)

Or can be rearranged as:

x = √2x - sin x - ex





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