Numerical Methods for Partial Differential Equations
Code no: 188.8.131.52.2.9 (9181) Semester: 8th, Teaching hours: 4
Introductory example: Dirichlet problem. Weak form. Arithmetic solution with Finite Elements Method. Boundary Value Problems and Galerkin method: General week form. Lax-Milgram theorem. Galerkin method. Errors. Rayleigh-Ritz-Galerkin method. General derivatives and Sobolev spaces. Green formulas. Elliptic boundary value problems. Existence and uniqueness. Applications. Finite Elements Methods for Elliptic Boundary Value Problems: Piecewise polynomial, Hermite and spline interpolation. Error estimates. Applications. Finite Elements Methods for Evolutionary Boundary Value Problems: Parabolic and hyperbolic problems. Euler and Crank-Nicholson methods. Stability. Error estimate. Applications. Finite Difference Methods: Sturm-Liouville and Dirichlet problems. Heat equation. Wave equation. Stability and Convergence. Workshop Exercises: Use of software (FORTRAN - IMSL, Matlab, Mathematica, Programming Libraries etc.) for programming.