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1 Initial and Boundary value problems; classification, well-posed problem.
2 Finite difference method, discretization, Finite difference approximation to derivatives.
3 The stability and convergence of finite difference method.
4 Convergence (Lax equivalent theorem), Fourier method and Matrix method for stability,
Compatibility.
5 Parabolic equations, an explicit finite difference approximation to one dimensional diffisuion
equation.
6 Crank-Nicolson implicit method, Iterative point methods, Jacobi, Gauss-Seidel method.
7 Hyperbolic equations; The quasilinear system.
8 Method of characteristics, Explicit finite Difference method.
9 MacCormics Method, Relaxation method, CFL condition, Lax-Wendroff method.
10 Elliptic equations; Laplace equation, Error analysis by using the maximum principle.
11 Solutions of finite difference equations.
12 Finite volume method.
13 Finite element method.
14 Initial and Boundary value problems; classification, well-posed problem. |