Course: Numerical Solution of Differencial Equations 2

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Course title Numerical Solution of Differencial Equations 2
Course code KMA/NDR2
Organizational form of instruction Lecture + Seminar
Level of course Master
Year of study not specified
Semester Summer
Number of ECTS credits 4
Language of instruction Czech
Status of course Compulsory-optional, Optional
Form of instruction Face-to-face
Work placements This is not an internship
Recommended optional programme components None
Lecturer(s)
  • Ženčák Pavel, RNDr. Ph.D.
Course content
1.The discretization of the second order boundary value problem using finite difference method. 2.The convergence of finite difference method for boundary value problems. 3.Solving ordinary differential equations and elliptic differential problems using collocation method. 4.Solution of elliptic problems using the finite difference method - methods of discretization. 5.The convergence of finite difference method and effect of different discretization. 6.The method of lines for parabolic and hyperbolic equations. Convergence of the method of lines. Using the method of lines for elliptic equations. The Rothe method for parabolic problem. 7.The finite difference method for parabolic problems - explicit and implicit methods and their properties. Conditional and unconditional stability of the methods. 8.Finite difference method for the parabolic problem in two spatial variables - generalization of basic methods and their efficiency comparison. 9.Alternating direction implicit methods and locally one-dimensional methods for solving parabolic problem in two spatial variables. 10.Characteristics of partial differential equations and the method of characteristics for hyperbolic problems. 11.Finite difference methods for hyperbolic first order problems and their stability. 12.Implicit finite difference methods and alternating direction implicit methods for solving hyperbolic problems

Learning activities and teaching methods
Monologic Lecture(Interpretation, Training), Demonstration
  • Semestral Work - 20 hours per semester
  • Attendace - 39 hours per semester
  • Preparation for the Exam - 60 hours per semester
Learning outcomes
The course introduces numerical methods for solving partial differential equations.
Comprehension Understand the numerical methods for solution of partial differential equations.
Prerequisites
Basic knowledge of numerical methods, theory of differential equations and programming in Matlabu, knowledge of basic numerical methods for solving ordinary differential equations.
KMA/NDR1 and KMA/PDR2

Assessment methods and criteria
Oral exam, Seminar Work

Credit: course work (including program development). Exam: the student has to understand the subject and be able to prove the principal results.
Recommended literature
  • E. Vitásek. (1994). Základy teorie numerických metod pro řešení diferenciálních rovnic. Academia, Praha.
  • J. W. Thomas. (1995). Numerical partial differential equations. Springer.
  • Morton, K. W., & Mayers, D. F. (2005). Numerical solution of partial differential equations: an introduction. Cambridge: Cambridge University Press.
  • S. Míka, P. Přikryl. (1996). Numerické metody řešení PDR II. ZČU Plzeň.
  • S. Míka, P. Přikryl. (1995). Numerické metody řešení PDR I. ZČU Plzeň.


Study plans that include the course
Faculty Study plan (Version) Branch of study Category Recommended year of study Recommended semester
Faculty of Science Applied Mathematics (2014) Mathematics courses 1 Summer
Faculty of Science Applications of Mathematics in Economy (2015) Mathematics courses - Summer
Faculty of Science General Physics and Mathematical Physics (2014) Physics courses 1 Summer