I have a polynomial equation which needs to be solved programmatically. The equation is as below.
x/207000 + (x/1349)^(1/0.282) = (260)^2/(207000*x)
I need to solve for x. I am using javascript for this. Is there any library in javascript which can solve mathematical equation?
Some computer algebra systems in JavaScript can solve systems of polynomial equations. Using Algebrite, you can solve an equation like this one:
roots(x^2 + 2x = 4)
The roots of this equation are [-1-5^(1/2),-1+5^(1/2)].
It's also possible to solve systems of polynomial equations using Nerdamer. Its documentation includes this example:
var sol = nerdamer.solveEquations('x^3+8=x^2+6','x');
console.log(sol.toString());
//1+i,-i+1,-1
There are JavaScript solvers out there that will numerically solve your problem. The non-linear solver that I know of is Ceres.js. Here is an example adapted to your question. The first thing we have to do is rearrange to the form F(x)=0.
x0 = 184.99976046503917
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8"/>
</head>
<body>
<h2>User Function</h2>
<p>This is an example of the solution of a user supplied function using Ceres.js</p>
<textarea id="demo" rows="40" cols="170">
</textarea>
<script type="module">
import {Ceres} from 'https://cdn.jsdelivr.net/gh/Pterodactylus/Ceres.js@master/Ceres-v1.5.3.js'
var fn1 = function f1(x){
return x[0]/207000 + Math.pow((x[0]/1349),(1/0.282)) - Math.pow((260),2)/(207000*x[0]);
}
let solver = new Ceres()
solver.add_function(fn1) //Add the first equation to the solver.
solver.promise.then(function(result) {
var x_guess = [1] //Guess the initial values of the solution.
var s = solver.solve(x_guess) //Solve the equation
var x = s.x //assign the calculated solution array to the variable x
document.getElementById("demo").value = s.report //Print solver report
solver.remove() //required to free the memory in C++
})
</script>
</body>
</html>
