TANA60	Numerical Solution of Partial Differential Equations, 3 ECTS-points /Numerisk lösning av partiella differentialekvationer/ Advancement level: D
	Aim: The course provides basic knowledge about the finite difference method for the solution of partial differential equations. The course also gives practical familarity with numerical computations on computers with examples taken from science and technology. Prerequisites: TANA 50 Numerical Methods II Supplementary courses: TANA 77 Scientific computations Course organization: In the computer assignments, we solve some practical problems numerically. The fundamental theory will be presented in the lectures and exemplified in the tutorials. Course content: Classification of partial differential equations. Boundary conditions, initial conditions, well-posed problems, finite difference approximations, local truncation error. Elliptic equations: maximum principle, barrier-lemma, convergence. Parabolic equations: stability, Lax' convergence theorem. Hyperbolic equations: the Courant-Friedrichs-Lewy condition for convergence. Iterative solution of sparse systems of equations, preconditioning, convergence rate estimates. Course literature: Will be specified in the course information
TEN1	Written examination, 2,5 p.
LAB1	Labratory work, 0 p.

Course language is swedish.