Abstract
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 Picard's method for the determination of the number of roots of a nonlinear equation along a finite interval and a relevant formula for the determination of such a root. Alternatively, it can be considered to be based on the method of integration by parts. The present method leads to a very simple non-iterative approximate formula, based on the classical Gauss quadrature rule for the computation of the sought root. The convergence of the method, for increasing values of the number of nodes n, is proved and numerical results for two transcendental equations are presented.
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