Numerical Method20815 marksNumerical: Poisson equation finite differenceLaplacian equation and Poisson's equation
Solve the Poisson equation with boundary conditions:
Solve the Poisson equation with boundary conditions:
$$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = -64xy, \quad 0 \leq x \leq 1, ; 0 \leq y \leq 1$$
$$u(0,y) = 0, ; u(x,0) = 0, ; u(1,y) = 150, ; u(x,1) = 150, ; h = \frac{1}{3}$$
[5]
PDE: $$\frac{\partial^2 u}{\partial x^2} + \frac{\partial^2 u}{\partial y^2} = -64xy, \quad 0 \le x \le 1,\ 0 \le y \le 1$$ So $f(x,y) = -64xy$. Boundary Conditions: - $u(0,y) = 0$ (left) - $u(x,0) = 0$ (bottom) - $u(1,y) = 150$ (right) - $u(x,1) = 150$ (top) Step size: $h = \frac{1}{3}$ --- With...