Numerical Methods20795 marksNumerical: Heun's method ODEHeun's method for ODE solving
Find the approximate value of y when x = 0.6 of dy/dx = 1-2xy, given that y = 0 when x = 0 with h=0.2 using Heun's method.
Find the approximate value of y when x = 0.6 of $dy/dx = 1-2xy$, given that y = 0 when x = 0 with h=0.2 using Heun's method. [5]
- ODE: $\frac{dy}{dx} = f(x,y) = 1 - 2xy$ - Initial condition: $y = 0$ at $x = 0$ - Step size: $h = 0.2$ - Target: $y$ at $x = 0.6$ (requires 3 steps) Heun's formulas: $$y^{n+1} = yn + h,f(xn, yn)$$ $$y{n+1} = yn + \frac{h}{2}\left[f(xn, yn) + f(x{n+1}, y^{n+1})\right]$$ $$k1 = f(0,0) = 1 - 0 = ...