Applied numerical methods II, 2D1250
Applied numerical methods is a master level course where the students
formulate, use, analyze
and implement advanced numerical methods to solve mathematical problems from
different applications in science and engineering.
The student learns to use and analyze the most important algorithms
for solving systems of equations and differential equations. To use means to
implement and choose a good method for
a given problem. The analysis focuses on accuracy and computational
efficiency of the method.
More precisely the goal means that the student can:
- formulate and analyze direct and iterative methods for linear and non
linear systems of equations and eigenvalue problems;
- derive global error estimates for approximation of differential equations
based on the local error of the method;
- construct and with error analysis motivate adaptive and implicit methods
for differential equations;
- derive and understand the relation between stability, consistency and
convergence for well posed differential equations;
- formulate and analyze finite element and finite difference methods for
some partial differential equations;
- formulate and use efficient hierarchical methods to solve differential
equations and integral equations.
Prerequisite:
The prerequisite for the course is linear algebra, calculus, differential
equations
and numerical methods corresponding to the first two years at KTH.
Examination:
During the course, the work of the student is focused on
problem solving in home work and projects with computer exercises, for
training to solve applied problems with numerical methods; the other half of
the course credit comes from a written exam.