Course description

Aim. Study of basic numerical methods from algorithmic and theoretical views.

Short description. The following basic chapters of numerical methods are considering: interpolation, approximation in normalized spaces, numerical differentiation, numerical integration, numerical solution of nonlinear equations, numerical methods for Cauchy problem, numerical solution of boundary value problems for ordinary differential equations, numerical solution of integral equations, numerical solution of boundary value problems for partial differential equations.    The main attention is concentrated on rigorous problems statement, the investigation of their well-possedness, the ideas of method building, the proof of convergence and the error estimate. The study is based on the knowledge of mathematical and functional analysis, linear algebra etc.

Objects. To be familiar with basic numerical methods including their theoretical analysis and algorithmic aspects.

As result after the study student must

• know: numerical methods of: analysis, solution of nonlinear equations and systems, Cauchy problems and boundary value problems for ordinary differential equations, boundary value problems for partial differential equations;
• be able: to choose and to apply numerical methods for the solution of various applied problems, to analyze their convergence and to estimate their error, to build own program products.