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 onedimensional 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.
