A non-iterative method for solving non-linear equations

摘要

In this paper, using a hyperbolic tangent function tanh(βx), β > 0, we develop a non-iterative method to estimate a root of an equation f(x) = 0. The problem of finding root is transformed to evaluating an integral, and thus we need not take account of choosing initial guess. The larger the value of β, the better the approximation to the root. Alternatively we employ the signum function sgn(x) instead of the hyperbolic tangent function, which results in an exact formula for the root. Availability of the present method is shown by some numerical examples for which the traditional Newton’s method is not appropriate.