Virtual Labs

Runge Kutta method 2nd order is used to solve _______________________

a: initial value disfferential equation Explanation

Explanation

b: boundry value disfferential equation Explanation

Explanation

c: Explanation

Explanation

d: Explanation

Explanation

The formulation used in Runge Kutta method 2nd order is

s_{y1} = hf(x_1, y_1, z_1)\ \ \ \ \ s_{z1} = hg(x_1, y_1, z_1)

s_{y2} = hf(x_1+h, y_1+s_{y1}, z_1+s_{z1})

s_{z2} = hf(x_1+h, y_1+s_{y1}, z_1+s_{z1})

y_2 = y_1 -\frac{s_{y1}-s_{y2}}{2} \ \ \ \ \ z_2 = z_1-\frac{s_{z1}-s_{z2}}{2}

Explanation

s_{y1} = hf(x_1, y_1, z_1)\ \ \ \ \ s_{z1} = hg(x_1, y_1, z_1)

s_{y2} = hf(x_1+h, y_1+s_{y1}, z_1+s_{z1})

s_{z2} = hf(x_1+h, y_1+s_{y1}, z_1+s_{z1})

y_2 = \frac{s_{y1}+s_{y2}}{2} \ \ \ \ \ z_2 = \frac{s_{z1}+s_{z2}}{2}

Explanation

s_{y1} = hf(x_1, y_1, z_1)\ \ \ \ \ s_{z1} = hg(x_1, y_1, z_1)

s_{y2} = hf(x_1+h, y_1+s_{y1}, z_1+s_{z1})

s_{z2} = hf(x_1+h, y_1+s_{y1}, z_1+s_{z1})

y_2 = y_1 +\frac{s_{y1}+s_{y2}}{2} \ \ \ \ \ z_2 = z_1+\frac{s_{z1}+s_{z2}}{2}

Explanation

s_{y1} = hf(x_1, y_1, z_1)\ \ \ \ \ s_{z1} = hg(x_1, y_1, z_1)

s_{y2} = hf(x_1+h, z_1+s_{z1})

s_{z2} = hf(x_1+h, z_1+s_{z1})

y_2 = y_1 +\frac{s_{y1}+s_{y2}}{2} \ \ \ \ \ z_2 = z_1+\frac{s_{z1}+s_{z2}}{2}

Explanation

ODE: Runge Kutta 2nd method for 2nd order equation (System of ODE)