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| NMAC16 | Numerical solution of differential equations, 5 p (sw) /Numerisk lösning av differentialekvationer/ Advancement level: C | |
| Aim: To give an overview of numerical methods for the solution of ordinary and partial differential equations and to prevent the theory needed to analyse the methods. To give practical experience of the methods through computer experiments. Prerequisites: Knowledge of mathematics and numerical analysis as taught in the first two years of the mathematics program and Numerical linear algebra and optimization,5 p.Course organization: The course consists of lectures, lessons and computer exercises.Course content: Ordinary differential equations: Linear multistep mehods: stability, consistency, convergence.Stiff differential equations. Runge-Kutta-methods. Error estimation and stepsize control. Partial differential equations: Classification. Wellposedness. Characteristics. Constistency. Convergence. Stability analysis. Explicit and implicit difference methods for parabolic equations. Iterative methods for elliptic problems. Application of the methods in computer exercises.Course literature: Dahlquist-Björck: Numerical Methods - Ch. 3.2 and 13. G. D. Smith: Numerical solution of partial differential equations. Finite Difference Methods. Oxford Applied Mathematics and Computing Science Series, 1985. J. D. Lambert: Numerical methods for ordinary differential systems. John Wiley & Sons, 1991 (complementary). A guide to MATLAB. Exercises and examples of earlier written examinations. | ||
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