Advanced Numerical Methods
|Ac.Year:||ukončen 2004/2005 (Not opened)|
|Language of Instruction:||Czech|
|Guarantor:||Baštinec Jaromír, doc. RNDr., CSc. (DMAT)|
|Faculty:||Faculty of Information Technology BUT|
|Department:||Department of Intelligent Systems FIT BUT|
| || ||The aim is to extend and intesify knowledge from the previous courses, namely in connexion with practical applications of the methods for solving the ordinary a partial differential equations. For this purpose two chapters summarizing the methods for solving linear and nonlinear equations precede.|
| || ||Numerical methods and modern algorithms for solving some technical problems. Solving the systems of linear and nonlinear equations. Numerical solutions of ordinary differential equations, initial value problems, one-step and multi-step methods, Taylor series method, extremely accurate calculations, automatization of input data, special simulation language and practical applications, boundary value problems. Partial differential equations, numerical investigation of fields.|
|Learning outcomes and competencies:|
| || ||The student is acquainted with some numerical methods for soluting the ordinary and partial differential equations.|
|Syllabus of lectures:|
- Numerical methods, principle, classification of errors, giving precision to results.
- Linear equations, finite, matrix-iterative and gradient-iterative methods.
- Nonlinear methods, review of nethods for one equation.
- Newton and iterative methods for systems.
- Ordinary differential equations, initial value problems, one-step methods.
- Multi-step methods.
- Taylor series method, possibilities of its application.
- Boundary value problems, finite difference method.
- Finite element methods, applications.
- Finite volume method.
- Partial differential equations, classification.
- Finite difference method, finite element method.
- Finite volume method, method of lines.
|Syllabus of laboratory exercises:|
| ||Laboratory and numerical exercises fulfilling the lectures.|
| || ||Laboratory work, tests ... maximum 20 points, project ... maximum 20 points, written term exam ... maximum 60 points.|