29
Persamaan Diferensial Parsial Finite Difference Approximation: Elliptic Equations Joko Wintoko Kuliah Matematika Teknik Kimia 2 JTK/FT/UGM/2011
Persamaan Diferensial ParsialFinite Difference Approximation: Elliptic Equations
Joko WintokoKuliah Matematika Teknik Kimia 2
JTK/FT/UGM/2011
Partial Differential Equation
Linear Second Order PDEs
• General form:
Linear Second Order PDEs
Elliptic PDEs
Parabolic PDEs
Hyperbolic PDEs
FINITE DIFFERENCE APPROXIMATION: ELLIPTIC EQUATIONS
Partial Differential Equations
Example of Elliptic PDEs
• Laplace equation
• Poisson Equation
FDA for Laplace Equation for 2D heat transfer
FDA for Laplace Equation for 2D heat transfer
Substituting into the original equation:
FDA for Laplace Equation for 2D heat transfer
FDA for Laplace Equation for 2D heat transfer
A
FDA for Laplace Equation for 2D heat transfer
FDA for Laplace Equation for 2D heat transfer
The Liebmann Method
• Gauss-Siedel approach that is applied to PDEs.
The Liebmann Method
Example 1
Example 1, contd.
Example 1, contd.
Example 1, contd.
Example 1, contd.
Derivative boundary condition(Neumann boundary condition)
Derivative boundary condition(Neumann boundary condition)
Derivative boundary condition(Neumann boundary condition)
Example 2
Example 2, contd.
Example 2, contd.
Example 2, contd.
