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- University
- Politecnico di Milano
- Degree programme
- Biomedical Engineering
- Subject
- Mathematical and Numerical Methods in Engineering
- Classification
- Notes · Complete set
- Original format
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NotesComplete set
Completed notes of the course Numerical Methods
Study material for Mathematical and Numerical Methods in Engineering, shared by the Studwiz community and reviewed by moderators.
Mathematical and Numerical Methods in EngineeringComplete set
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Numerical Methods Course held by Prof. Christian Vergara Year 2020-2021 Notes by Alessandro M. Ippoliti Leonhard Euler 1707-1783. 2 Contents I Finite Differences 5 1 General Overview 7 2 ODE Approximations 9 2.1 Approximations of the 1 st Derivative . . . . . . . . . . . . . . 9 2.1.1 Forward Euler Method . . . . . . . . . . . . . . . . . . 9 2.1.2 Backward Euler Method . . . . . . . . . . . . . . . . . 10 2.1.3 Central Approximation Formula . . . . . . . . . . . . . 10 2.1.4 Forward and Backward 2 nd Order Formulas . . . . . . 12 2.1.5 Approximations of the 2 nd Derivative . . . . . . . . . . 12 2.2 Solving the Cauchy Problem . . . . . . . . . . . . . . . . . . . 12 2.3 Model Evaluation Parameters . . . . . . . . . . . . . . . . . . 14 2.3.1 Consistency . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 Zero Stability . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . 16 2.3.4 Absolute Stability . . . . . . . . . . . . . . . . . . . . . 17 2.4 The Theta Method . . . . . . . . . . . . . . . . . . . . . . . . 19 2.5 The Advection Problem . . . . . . . . . . . . . . . . . . . . . 19 2.6 Solution through the Forward Euler Centered Method . . . . . 20 2.6.1 Consistency . . . . . . . . . . . . . . . . . . . . . . . . 21 2.6.2 Zero Stability . . . . . . . . . . . . . . . . . . . . . . . 22 2.6.3 Convergence . . . . . . . . . . . . . . . . . . . . . . . . 23 2.6.4 Absolute Stability . . . . . . . . . . . . . . . . . . . . . 23 2.7 The Upwind Method . . . . . . . . . . . . . . . . . . . . . . . 24 2.7.1 Consistency . . . . . . . . . . . . . . . . . . . . . . . . 24 2.7.2 Absolute Stability . . . . . . . . . . . . . . . . . . . . . 25 2.8 Numerical Viscosity . . . . . . . . . . . . . . . . . . . . . . . . 26…
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