secent.groovy

​def f(x){    // we are taking equation as x^3+x-1
    def  f = 2*x + x - 1;
    return f;
}
 
def secant(x1, x2, E) {
  
    def n = 0, xm, x0, c;

        while(true){
            // calculate the intermediate value
            x0 = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1));
 
            // check if x0 is root of equation or not
            c = f(x1) * f(x0);
 
            // update the value of interval
            x1 = x2;
            x2 = x0;
 
            // update number of iteration
            n++;
 
            // if x0 is the root of equation then break the loop
            if (c == 0)
                break;
            xm = (x1 * f(x2) - x2 * f(x1)) / (f(x2) - f(x1));
            if(Math.abs(xm - x0) >= E) continue;
            else break;
        } 
                                // until the convergence
       return x0.round(6)
        //document.write("Root of the given equation=" + x0.toFixed(6));
        //document.write("No. of iterations = " + n);
}

response = [];
response["transit"] = secant(0, 10, 0.000001);
​