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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References

SHOWING 1-10 OF 10 REFERENCES
Application of the Cauchy theorem to the location of zeros of sectionally analytic functions
SummaryA new method for the derivation of closed-form formulae for the zeros of sectionally analytic functions in the complex plane is proposed. This method is based on the Cauchy theorem in complex
Application of the gaus quadrature rule to the numberical solution of nonlinear equations
A new method for the solution of a single real nonlinear algebraic or transcendental equation with one simple root along a finite interval is proposed. This method is based on a modification of
A simple quadrature-type method for the computation of real zeros of analytic functions in finite intervals
A new direct approximate method for the computation of zeros of analytic functions is proposed. For such a function possessing one real zero in a finite part of the real axis, this method permits the
Modified gauss-jacobi quadrature formulas for the numerical evaluation of cauchy type singular integrals
We obtain modified Gauss-Jacobi quadrature formulas for the numerical evaluation of Cauchy principal values of integralsα,β>−1, wheref(x) possesses one or more simple poles in (−1, 1). Forα=β=±1/2,
Error Bounds for the Gauss-Chebyshev Quadrature Formula of the Closed Type
for some v E [-1, 1]. The error expression (2) is valid for the class of functions which are 2n-times differentiable. In most cases, the exact value of Xq will be unknown, and the estimate max <t?1
A new simple method for the analytical solution of Kepler's equation
A new simple method for the closed-form solution of nonlinear algebraic and transcendental equations through integral formulae is proposed. This method is applied to the solution of the famous Kepler
Methods of Numerical Integration
Numerical analysis