Question

Using Runge-Kutta's method of fourth order, find y(0.2) for the equation (dy)/(dx)=(y-x)/(y+x),y(0)=1, taking h=0.2.

Answer 1

To find y(0.2), we can use Runge-Kutta's method of fourth order. By iteratively calculating the k's and updating the y value, we can find the desired result.

Step-by-step explanation:

The question asks to find y(0.2) using Runge-Kutta's method of fourth order. To solve this, we can use the given initial condition y(0)=1 and step size h=0.2.

To apply the fourth-order Runge-Kutta method, we need to iterate through the steps:

1. Compute k1 using the given differential equation: k1=h*(y-x)/(y+x)
2. Compute k2: k2=h*((y+0.5*k1)-(x+0.5*h))/((y+0.5*k1)+(x+0.5*h))
3. Compute k3: k3=h*((y+0.5*k2)-(x+0.5*h))/((y+0.5*k2)+(x+0.5*h))
4. Compute k4: k4=h*((y+k3)-(x+h))/((y+k3)+(x+h))
5. Update y using the weighted average of the k's: y=y+(1/6)*(k1+2*k2+2*k3+k4)
6. Repeat steps 1-5 until reaching the desired x value (0.2 in this case)

By plugging in the given values into the equations and iteratively calculating the k's, we can find the value of y(0.2) using Runge-Kutta's method of fourth order.