# Questions tagged [rootfinding]

For questions about the theory and process of finding the roots of a function (values where the function returns zero).

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### Splitting system of equations into linear and nonlinear part and solving separately

I was working on a problem recently (calculating all flows in a network given input and output flows, basically what Hardy-Cross tries to achieve) which can be formulated as a well-determined system ...
1 vote
120 views

### Secant Method for finding $\sup f^{-1}(0)$

Let $f \in C^0[0, 1]$, and suppose $f \ge 0$. How can I compute $\sup f^{-1}(0)$ efficiently?
129 views

392 views

### What is an efficient way to calculate zeros of Bessel functions?

One approach is the brute force method of evaluating at all points at fixed intervals and when it nears zero write value, this can be combined with adaptive step size. Another approach is ...
106 views

### ODE Event detection for calculating multiple roots of continuous sinusoidal equation

I found a paper  that has a method for computing rise and set times of a satellite given a closed form solution. It is a complicated sinusoidal function and the paper has a method to calculate a ...
196 views

### How to avoid gsl root finder evaluate function outside its domain

When I use the newton's method or hybrid solver in the GSL package to deal with 1-D or multidimensional root solving problems, the code frequently crashes when the solver requests function value ...
88 views

### Robust ways to find zeros of the Tricomi confluent hypergeometric function as a function of its parameters

I'm solving a quantum mechanical problem, and the quantization condition requires me to solve the equation $$U\left(\frac12(\ell+1-E), \ell+1, r^2\right) = 0,$$ where $U(a,b,z)$ is the confluent ...
1 vote
152 views

### Finding curves where function goes to zero in two dimensions

Suppose $f(x,y)$ is a complex function of two real arguments with roots* that are not discrete points but lie in curves. (Is there are term for this characteristic?) An example is shown below: the ...