First partial exam Numerical method Sample text

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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…