| Code |
15615
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| Year |
1
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| Semester |
S1
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| ECTS Credits |
8
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| Workload |
TP(60H)
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| Scientific area |
Mathematics
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Entry requirements |
Does not have.
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Learning outcomes |
The main objective of this course is to develop in students the skills necessary to numerically solve problems involving differential equations with boundary values and partial derivatives, and to analyze and interpret the solutions thus obtained. In particular, it is intended that students acquire the theoretical and practical foundations related to finite difference methods, Galerkin and finite element method.
At the end of this course the student should be able to:
- Identify and apply numerical methods appropriate to the problem under study;
- Know the main advantages and disadvantages of the numerical schemes studied;
- Study the consistency and stability of a numerical scheme;
- Computationally implement the different numerical methods.
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Syllabus |
1. Ordinary differential equations with boundary values
1.1. Shooting method
1.2. Collocation method
1.3. Least squares method
1.4. Method of residuals
1.5. Variational formulation
1.6. Finite element method
1.7. Finite difference method
2. Differential equations with partial derivatives
2.1. Stationary problems
2.1.1. Finite difference methods – stability and convergence
2.1.2. Galerkin Methods – variational formulation, Lax-Milgram Theorem, Cea's Lemma
2.1.3. Finite element methods - mesh generation, element spaces, stability and convergence
2.2. Evolutionary Problems
2.2.1. Finite difference methods – stability and convergence
2.2.2. Galerkin methods – variational formulation, Caratheodory's Theorem
2.2.3. Finite element methods – stability and convergence
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Main Bibliography |
Larsson, Stig and Thomée, Vidar Partial differential equations with numerical methods. Texts in Applied Mathematics,45. Springer-Verlag, Berlin, 2003.
Lynch, Daniel R. Numerical Partial Differential Equations for Environmental Scientists and Engineers. Springer US,United States, 2005
Burden, Richard L. and Faires, J. Douglas and Burden, Annette M. Numerical Analysis, Cengage Learning, United States, 2016.
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Language |
Portuguese. Tutorial support is available in English.
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