Numerical Methods208010 marksNumerical: Shooting method ODEShooting method for boundary value problems
Solve the following ordinary differential equation using shooting method. y'' + xy' - xy = 2x with boundary conditions y(0) = 1 and y(2) = 10
Solve the following ordinary differential equation using shooting method. $y'' + xy' - xy = 2x$ with boundary conditions $y(0) = 1$ and $y(2) = 10$ [10]
- ODE: $y'' + xy' - xy = 2x$ - Boundary conditions: $y(0) = 1$, $y(2) = 10$ - Interval: $[0, 2]$ - Step size (chosen for hand computation): $h = 0.5$ (4 steps) - Integration method: Euler's method --- Let $y1 = y$, $y2 = y'$. Then: $$y1' = y2$$ $$y2' = y'' = 2x - xy' + xy = 2x - x y2 + x y1$$ Ini...