[nodejs][javascript]numerical analysis of differential equations

difffeq.js

// analysis of differential equations

// parameters
// f: differential equation dy/dx = f(x, y)
// y0, x0: initial values
// h: small value of diff x
// n: calc count, xn = x0 + n*h 

var eular = function (f, y0, x0, h, n) {
    var y = [y0], x = [x0];
    for (var i = 0; i < n; i++) {
        y[i + 1] = y[i] + h * f(x[i], y[i]);
        x[i + 1] = x[i] + h;
    }
    return {x: x, y: y};
};

// modified eular method
var eular2 = function (f, y0, x0, h, n) {
    var y = [y0], x = [x0];
    for (var i = 0; i < n; i++) {
        var d = y[i] + h * f(x[i], y[i]);
        y[i + 1] = y[i] + h / 2 * (f(x[i], y[i]) + f(x[i] + h, d));
        x[i + 1] = x[i] + h;
    }
    return {x: x, y: y};
};

var rk4 = function (f, y0, x0, h, n) {
    var y = [y0], x = [x0];
    for (var i = 0; i < n; i++) {
        var k1 = f(x[i], y[i]);
        var k2 = f(x[i] + h / 2, y[i] + h / 2 * k1);
        var k3 = f(x[i] + h / 2, y[i] + h / 2 * k2);
        var k4 = f(x[i] + h, y[i] + h * k3);
        y[i + 1] = y[i] + h / 6 * (k1 + 2 * k2 + 2 * k3 + k4);
        x[i + 1] = x[i] + h;
    }
    return {x: x, y: y};
};



// example
var f = function (x, y) {
    return x + 1;
};
// dy/dx = x + 1  ==> y = 1/2 * x^2 + x + y0

// check values
var c = {x: [0], y: [0]}
for (var i = 0; i < 10; i++) {
    var x =  0.1 * (i + 1);
    c.x.push(x);
    c.y.push(1 / 2 * x * x + x);
}
//console.log(c.y);

// eular
var e = eular(f, 0, 0, 0.1, 10);
//console.log(e.y);
console.log(e.y.map(function (y, i) {return y - c.y[i];}));

// eular2
var e2 = eular2(f, 0, 0, 0.1, 10);
//console.log(e2.y);
console.log(e2.y.map(function (y, i) {return y - c.y[i];}));

// runge kutta
var r = rk4(f, 0, 0, 0.1, 10);
//console.log(r.y);
console.log(r.y.map(function (y, i) {return y - c.y[i];}));