Numerical methods

Garant předmětu:

Lecturer:

Tutor:

Supervisor:

Department of Applied Mathematics

Synopsis:

The course introduces numerical methods essential for solution of differential equations. It includes fundamentals for solution of ordinary differential equations (ODE) under various initial and boundary conditions and partial differential equations (PDE) of elliptic and parabolic type. The course focuses on the practical use of numerical algorithms and an understanding of stability and instability of some numerical processes.

Requirements:

Syllabus of lectures:

1.Numerical evaluation of integrals.

2.Approximate solution of ordinary differential equations by one-step methods (Runge - Kutta).

3.Approximate solution of ordinary differential equations by n-step methods.

4.Stability of methods using higher n-step methods.

5.Boundary problem in ODE's (method of shooting).

6.Translation of boundary conditions.

7.Method of finite differences and finite elements method in 1-dimensional case.

8.Method of finite differences and finite elements method in n-dimensional case of elliptic type PDE's.

9.Algebraic equation solved using method of finite differences and finite elements method (fast iteration algorithms).

10.Multiple finite differences method for PDE's of elliptic type.

11.Evolution in parabolic PDE's - equation of diffusion.

12.Approximate solution of parabolic PDE's - conditional and unconditional stability.

13.Alternating methods for evolution problems.

14.Numerical algorithms and their complexity.

Syllabus of tutorials:

Study Objective:

Study materials:

Ralston A.: A first course in numerical analysis, McGraw-Hill, 1965

Rektorys K.: The Method of Discretisation in Time and Partial Differential Equations, Dordrecht, 1982

Note:

Further information:

No time-table has been prepared for this course

The course is a part of the following study plans: