Nonlinear Equation Solver

This application is for equations of one variable. If you want to solve systems of nonlinear equations or nonlinear least-squares problems, the calculator System of Nonlinear Equations is recommended.

Let $f(x)$ be a twice differentiable and real-valued function, this application find the roots $x^\star$ of $f$ such that \[ f(x^\star) = 0 \] by using a variant of Newton's method. In the calculation the solver uses both the first derivative and the second derivative of $f$ and they are calculated using Derivative Calculator. As a globally convergent solver, this calculator should be able to find the root $x^\star$ of $f$ from any initial guess $x_0$ which is not necessary to close to the root $x^\star$, but $x_0$ must be in the domain of $f$.

Input Data

The calculator uses the same input format as Derivative Calculator. It is not necessary to input $x_0$ if the interval $(0,1)$ is a subset of the domain of $f(x)$. If $x_0$ is not entered or the solver cannot find the root from $x_0$ input by users, new $x_0\in(0,1)$ will be generated automatically.

Nonlinear Equations Calculator

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