# An elementary noniterative quadrature-type method for the numerical solution of a nonlinear equation

@article{Ioakimidis2005AnEN, title={An elementary noniterative quadrature-type method for the numerical solution of a nonlinear equation}, author={Nikolaos I. Ioakimidis and Eleni G. Anastasselou}, journal={Computing}, year={2005}, volume={37}, pages={269-275} }

A simple noniterative method for the numerical determination of one simple root of a nonlinear differentiable algebraic or transcendental function along a finite real interval is proposed. This method is based on the computation of an integral involving the above function both by the Gauss- and the Lobatto-Chebyshev quadrature rules for regular integrals and equating the obtained results. The convergence of the method is proved under mild assumptions and numerical results for two classical…

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