Title:

# Advanced Numerical Methods

Code:MNM
Ac.Year:ukončen 2004/2005 (Not opened)
Sem:Summer
Language of Instruction:Czech
Credits:6
Completion:examination (written)
Type of
instruction:
Hour/semLecturesSeminar
Exercises
Laboratory
Exercises
Computer
Exercises
Other
Hours:26130260
ExamsTestsExercisesLaboratoriesOther
Points:6004000
Guarantor:Baštinec Jaromír, doc. RNDr., CSc. (DMAT)
Faculty:Faculty of Information Technology BUT
Department:Department of Intelligent Systems FIT BUT
Prerequisites:
 Mathematical Analysis 1 (MA17), DMATH Mathematical Analysis 2 (M2I8), DMAT

Learning objectives:
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.
Description:
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.
Exam prerequisites:
Laboratory work, tests ... maximum 20 points, project ... maximum 20 points, written term exam ... maximum 60 points.