The main purpose of this course is learning numerical methods useful in finding approximate solutions of ordinary as well as partial differential equations.
Prerequisites
Knowledge of the following courses: Numerical Methods 1 and Ordinary Differential Equations
Scope
Numerical solution of ordinary differential equations - the existence and uniqueness of solutions, application of the Taylor formula, multistep methods, Runge-Kutta methods, local and global errors, stability and convergence, systems of differential equations, boundary problems, stiff problems.
Numerical solution of partial differential equations - parabolic, elliptic and hyperbolic equations, finite difference method, methods of discretization of differential equations, explicit and implicit methods, analysis of the stability and convergence of schemes, introduction to finite element and finite volume methods.
Teaching methods
Traditional lectures, classes with solving of problems related to the subjects considered during lectures, laboratory exercises in the computer lab.
Learning outcomes and methods of theirs verification
Outcome description
Outcome symbols
Methods of verification
The class form
Assignment conditions
Lecture: Positive passing of written exam (before taking the exam a student must gain positive grades from the class as well as the laboratory).
Class: Positive passing of two tests.
Laboratory: Positive passing of two tests.
Calculation of the final grade: lecture 50% + class 25% + laboratory 25%
Recommended reading
D. Kincaid, W. Cheney, Numerical Analysis: Mathematics of Scientific Computing, American Mathematical Soc., 2009
