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MAT 488E - PDE:Numerical Sol.

Course Objectives

1. To introduce the basic concepts of the solutions of the partial differential equations,
2. To teach numerical methods to solve partial differential equations of various types.

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

Course Coordinator
Ersin Özuğurlu
Course Language
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