Question

I am trying to solve the next equation with C++ help: 3sin(sqrt(x)) + 0.35x – 3.8 = 0
The area with solution is [2, 3]

I wrote next code:

float f(float x)
{
    return (3 * sin(sqrt(x))) + (0.35 * x) - 3.8; //this is equation i am trying to solve
}

float g(float x, float(*f_ptr)(float)) 
{
    const float CONST = 0.1f; //const used to solve equation

    return CONST * f_ptr(x) + x;
}

void Task4_CalculateSomething()
{
    float x0, //starting aproximation
        xk, //current aproximation
        a = 2, //left barrier
        b = 3, //right barrier
        epsilon = 0.001; //allowed error

    const float REAL_SOLUTION = 2.2985; //real solution of selected equation

    printf("Setup starting aproximation: ");
    scanf("%f", &x0);

    do
    {
        xk = g(x0, f); //calc current aproximation

        if (fabs(xk - x0) < epsilon) //if Xn - Xn-1 fits the allowed error, the solution must be found
            break; //then we exit
        else
            x0 = xk; //else reset x values
    }
    while (fabs(a - x0) > epsilon && fabs(b - x0) > epsilon);

    printf("Found solution: %f\nReal solution: %f\n", xk, REAL_SOLUTION);
}

But it gives me weird results like -1.#IND00 which i don’t even know what is it.
And i can’t find any error there…

Answer 1

Try using another algorithm like this:

1. Write the derivative of the function: der=1.5*cos(sqrt((x))/sqrt(x)+.35
2. next value is xk=x0-mysinc(x0)/der(x0)

in few steps will fall into the solution… or make your variable CONST have a dynamic value of -1/der(x).