Numerical Methods20805 marksNumerical: Poisson's equation solvingPoisson's equation and finite difference method
Solve the Poisson's equation ∂2f/∂x2+∂2f/∂y2=2x2y2\partial^2f/\partial x^2+\partial^2f/\partial y^2 = 2x^2y^2∂2f/∂x2+∂2f/∂y2=2x2y2 over the square domain 0<=x<=3 and 0<=y<=3 with f=0 on the boundary and h = 1.
Solve the Poisson's equation ∂2f/∂x2+∂2f/∂y2=2x2y2\partial^2f/\partial x^2+\partial^2f/\partial y^2 = 2x^2y^2∂2f/∂x2+∂2f/∂y2=2x2y2 over the square domain 0<=x<=3 and 0<=y<=3 with f=0 on the boundary and h = 1. [5]
- PDE: $\dfrac{\partial^2 f}{\partial x^2} + \dfrac{\partial^2 f}{\partial y^2} = 2x^2 y^2$, so $g(x,y) = 2x^2y^2$ - Domain: $0 \le x \le 3$, $0 \le y \le 3$ (square) - Boundary condition: $f = 0$ on all boundaries - Mesh spacing: $h = 1$ All data present. Proceed. --- With $h = 1$: nodes at