| Code |
Course Name |
Language |
Type |
| MAT 488E |
Numerical Solutions of PDE |
English |
Elective |
| Local Credits |
ECTS |
Theoretical |
Tutorial |
Laboratory |
| 3 |
6 |
3 |
0 |
0 |
| Course Prerequisites and Class Restriction |
| Prerequisites |
MAT 331 MIN DD
or MAT 331E MIN DD
or MAT 234 MIN DD
or MAT 234E MIN DD
|
| Class Restriction |
None |
| Course Description |
| Initial and boundary value problems; Classification, Well-posed problem. Finite difference method, Discretization, Finite
difference approximation to derivatives, The stability and convergence of finite difference method, Convergence (Lax
equivalent theorem), Fourier method and Matrix method for stability, Compatibility. Parabolic equations, An explicit finite
difference approximation to one dimensional diffusion equation, Crank-Nicolson implicit method, Iterative point methods,
Jacobi, Gauss-Seidel method. Hyperbolic equations; The quasilinear system, Method of characteristics, Explicit finite difference
method, MacCormics Method, Relaxation method, CFL condition, Lax-Wendroff method. Elliptic equations; Laplace equation,
Error analysis by using the maximum principle, Iterative methods, Solutions of finite difference equations. Other methods;
Finite volume method, Finite element method, Spectral method. |
|
