#NumMeth Lab 6 (Diff. Eq) COMPLETE

N = 11;

var y = x => 3*x*x*x;
var dy = x =>  9*x*x;
var ddy = x =>  18*x;

var pFunc = x =>  1;
var qFunc = x => -1;

x_A = 1.0;
x_B = 2.0;

y_A = y(x_A);
y_B = y(x_B);

h = (x_B - x_A) / (N - 1);

f = [], q = [], p = []; //size = n

function solveMatrix(n, a, b, c, d) {
    var alpha = [], beta = [], res = []; //size = n

    alpha[0] = -c[0] / b[0];
    beta[0] = d[0] / b[0];

    for (var i = 1; i < n; i++) {
        alpha[i] = (-c[i]) / (a[i] * alpha[i-1] + b[i]);
        beta[i] = (d[i] - a[i] * beta[i-1]) / (a[i] * alpha[i-1] + b[i]);
    }
    res[n-1] = beta[n-1];

    for (var i = n-2; i >= 0; i--) res[i] = alpha[i] * res[i+1] + beta[i];

    return res;
}

function countFunc(n) {
    for (var i = 0; i < n; i++) {
        var x = x_A + i*h;
        f[i] = ddy(x) + pFunc(x)*dy(x) + qFunc(x)*y(x);
        p[i] = pFunc(x);
        q[i] = qFunc(x);
    }
}

function solveEquation(n) {

    var a = [], b = [], c = [], d = []; //size = n-2
    var e = [], res = [];               //size = n

    for (var i = 1; i < n-3; i++) {

        a[i] = 1 - p[i+1]*h/2;
        b[i] = q[i+1]*h*h - 2;
        c[i] = 1 + p[i+1]*h/2;
        d[i] = f[i+1]*h*h;
    }

    a[0] = 0;
    b[0] = q[1]*h*h - 2;
    c[0] = 1 + p[1]*h/2;
    d[0] = f[1]*h*h - y_A*(1 - p[1]*h/2);

    a[n-3] = 1 - p[n-2]*h/2;
    b[n-3] = q[n-2]*h*h - 2;
    c[n-3] = 0;
    d[n-3] = f[n-2]*h*h - y_B*(1 + p[n-2]*h/2);

    e = solveMatrix(n-2, a, b, c, d);

    for (var i = 0; i < n-2; i++) res[i+1] = e[i];
    res[0] = y_A;
    res[n-1] = y_B;

    var resStr6 = "res:";
    var texStr6 = "\\hline\n";
    for (var i = 0; i < n; i++) {
        resStr6 +=  "[" + i + "]: x:" + (x_A + i*h) +
                                " y:" + y(x_A + i*h) +
                                " res:" + res[i] +
                                " d:" + Math.abs(y(x_A + i*h) - res[i]) + "\n";
        texStr6 += (x_A + i*h) + " & " +
                    y(x_A + i*h).toFixed(6) + " & " +
                    res[i].toFixed(6) + " & " +
                    Math.abs(y(x_A + i*h) - res[i]).toFixed(6) + " \\\\ " + "\n" + "\\hline" + "\n";
    }

    console.log(resStr6);
    console.log(texStr6);
}

function lab6Main() {
    countFunc(N);
    solveEquation(N);
}