University study material for Mathematical and Numerical Methods in Engineering in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: EXAMPLE 1 OF EXAM - NUMERICAL METHODS Prof. C. Vergara TIME : 1h 45' Rispondere direttamente su Forms o su un foglio di carta in base alle istruzioni indicate punto per punto. Per le risposte scritte su un foglio di carta, eseguire poi la scansione e il caricamento su Forms solo
University study material for Mathematical and Numerical Methods in Engineering in the Biomedical Engineering degree programme at Politecnico di Milano. The document covers: EXAMPLE 1 OF EXAM - NUMERICAL METHODS Prof. C. Vergara TIME : 1h 45' Rispondere direttamente su Forms o su un foglio di carta in base alle istruzioni indicate punto per punto. Per le risposte scritte su un foglio di carta, eseguire poi la scansione e il caricamento su Forms solo
Import quality: text was extracted directly from the original document.
Representative passages recognised in different parts of the material. The full extracted text remains available to search, while this compact preview makes the page easier to read.
EXAMPLE 1 OF EXAM - NUMERICAL METHODS Prof. C. Vergara TIME : 1h 45' Rispondere direttamente su Forms o su un foglio di carta in base alle istruzioni indicate punto per punto. Per le risposte scritte su un foglio di carta, eseguire poi la scansione e il caricamento su Forms solo alla fine della prova, nel momento in cui vi verrà esplicitamente richiesto o chiedere il permesso al docente --------------------------------------------------------------------------------------------------------------------- --------------- Respond directly on Forms or on a sheet of paper according to the step-by-step instructions. For answers written on a sheet of paper, then scan and upload to Forms only at the end of the test, when you are explicitly asked or ask for this to the teacher Pontos:6/33 Part I Quiz Answer to the following questions: Correto 1/1 Pontos Which of the following is the Upwind scheme for a conservation law with convection given by beta<0? 1 = (1−Δ𝑡𝛽/ℎ)( − )𝑈𝑛+1𝑗 𝑈𝑛𝑗+1 𝑈𝑛𝑗−1 = (1−Δ𝑡𝛽/ℎ)( − )𝑈𝑛+1𝑗 𝑈𝑛𝑗 𝑈𝑛𝑗−1 = − ( − )+ ( −2 + )𝑈𝑛+1𝑗 𝑈𝑛𝑗 Δ𝑡𝛽 ℎ 𝑈𝑛𝑗 𝑈𝑛𝑗−1 Δ𝛽2 𝑡2 2ℎ2 𝑈𝑛𝑗+1 𝑈𝑛𝑗 𝑈𝑛𝑗−1 28/12/2024, 19:39 EXAMPLE 1 OF EXAM - NUMERICAL METHODS https://forms.office.com/Pages/ResponsePage.aspx?id=K3EXCvNtXUKAjjCd8ope66irfrBtR-9Mn7CDwbBlTypUOFI1QU9KUjFNVUMyVkFOVkxQ… 1/9 = − ( − )+ ( −2 + )𝑈𝑛+1𝑗 𝑈𝑛𝑗 Δ𝑡𝛽 2ℎ 𝑈𝑛𝑗+1 𝑈𝑛𝑗−1 |𝛽|Δ𝑡 2ℎ 𝑈𝑛𝑗+1 𝑈𝑛𝑗 𝑈𝑛𝑗−1 Correto 1/1 Pontos Which sentence is true about the Backward Euler Centered method for the advection problem? 2 It is stable provided that the CFL condition is satisfied; Requires the solution of a linear system with a symmetric matrix It does not require an initial condition Always (absolutely) stable for any ℎ and Δ𝑡; Correto 1/1 Pontos The Backward Euler approximation of the heat equation in algebraic form is given by (A is the matrix…
First page of the document.
