| TANA31 |
Computational Methods for Ordinary and Partial Differential Equations, 6 ECTS credits.
/Beräkningsmetoder för ordinära och partiella differentialekvationer/
For:
M
MMAT
Y
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Prel. scheduled
hours: 50
Rec. self-study hours: 110
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Area of Education: Science
Main field of studies: Mathematics, Applied mathematics
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Advancement level
(G1, G2, A): A
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Aim:
Many important problems from technology, science and economics are formulated in terms of differential equations. Thus it is important to be able to solve such equations accurately and efficiently. In the course we treat finite difference approximations of partial differential equations and numerical methods for solving ordinary differential equations. The theory is illustrated by using problems from relevant applications.
After a completed course the student should be able to
- discuss important concepts
- derive difference approximations of derivatives with desired properties and explain how boundary conditions should be treated numerically.
- explain and use standard methods, in particular Runge-Kutta type methods, for solving time dependent problems.
- explain what stiffness is and use implicit time stepping methods for solving stiff problems.
- explain the requirements on the computational mesh that need to be fulfilled in order for a finite difference solution to give a good solution.
- write Matlab programs that solves different types of partial differential equations.
- judge the quality of a numerical solution
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus in several variables, Linear algebra and some skills in programming.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Organisation:
Lectures, lessons and computer exercises
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Course contents:
Classification of differential equations, order of accuracy, consistency, convergence, wellposedness, stability, stability analysis using the Fourier ansatz.
Ordinary differential equations: Runge-Kutta methods, explicit and implicit methods, stiff problems
Partial differential equations: finite difference methods, interpolation of boundary conditions, Crank-Nicholson method.
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Course literature:
High Order Difference Methods for Time Dependent PDE, Bertil Gustafsson, Springer 2008
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Examination: |
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Written examination
Laboratory work
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4 ECTS
2 ECTS
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Course language is English.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Fredrik Berntsson
Link to the course homepage at the department
Course Syllabus in Swedish
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