Solve fracdydx = fracxy, y(0) = 1, at x = 0.4 using Runge-Kutta's 4th | Numerical Method 2081

Numerical Method20815 marksNumerical: Runge-Kutta 4th order methodRunge-Kutta methods

Solve $\frac{dy}{dx} = \frac{x}{y}$ , $y(0) = 1$ , at $x = 0.4$ using Runge-Kutta's 4th order method. [5]

Solve $\frac{dy}{dx} = \frac{x}{y}$, $y(0) = 1$, at $x = 0.4$ using Runge-Kutta's 4th order method. [5]

$\frac{dy}{dx} = f(x,y) = \frac{x}{y}, \quad y0 = 1 \text{ at } x0 = 0, \quad \text{find } y(0.4)$ Step size: $h = 0.4$ (single step). $k1 = h f(x0, y0)$ $k2 = h f\left(x0+\tfrac{h}{2}, y0+\tfrac{k1}{2}\right)$ $k3 = h f\left(x0+\tfrac{h}{2}, y0+\tfrac{k2}{2}\right)$ $$k4 = h f\left(x0+h,...

$$\frac{dy}{dx} = f(x,y) = \frac{x}{y}, \quad y0 = 1 \text{ at } x0 = 0, \quad \text{find } y(0.4)$$ Step size: $h = 0.4$ (single step). $$k1 = h f(x0, y0)$$ $$k2 = h f\left(x0+\tfrac{h}{2}, y0+\tfrac{k1}{2}\right)$$ $$k3 = h f\left(x0+\tfrac{h}{2}, y0+\tfrac{k2}{2}\right)$$ $$k4 = h f\left(x0+h,...

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Solve fracdydx = fracxy, y(0) = 1, at x = 0.4 using Runge-Kutta's 4th order method.