Tutorial quiz 11.pdf - ESO 208A Computational Methods in Engineering Tutorial Quiz 11 Duration 15 min Name Roll No 06.11.19 Section Instructions Show

Tutorial quiz 11.pdf - ESO 208A Computational Methods in...

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ESO 208A: Computational Methods in Engineering Tutorial Quiz 11 Duration: 15 min 06.11.19 Name: Roll No: Section: Instructions: Show all calculations. An answer, without any supporting calculations, will bear zero credit even if it were correct. No credit for solving by any other method than asked. Perform calculations using infinite precision but report your intermediate and final calculations upto 4 significant digits with rounding. Q1 [8] Solve the differential equation 𝑑𝑦 𝑑𝑡 + ? ? = ? 𝑒 −𝑡 , with the initial condition y (0) = 0. Here, a and b are the two smallest non-zero digits of your roll no such that a < b . For eg., if roll number is 180401 then a = 1; b = 4.
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Unformatted text preview: Use Heun ’ s method by following the steps outlined below a) Obtain the predictor-corrector algorithms for this method for a generic time-step ‘ n ’ . [4] b) Solve for y (0.5) using single corrector application with a time step of 0.5. [4] b) [7] Reduce the following differential equation into a set of linear equations in y using Direct Method with 1 st order forward difference approximation and h = 1 for ? ∈ [0,3]; ?(0) = 1; ?(3) = 2 : ? ′′ + ?? − ?? = 0 , where a and b are as obtained in Q1(a). Leave your final answer in matrix form with known coefficients and unknown y is . Do not solve the matrix. Algorithms given which may/ may not be useful:...
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