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Consider the linear transport equation
Ë™ c(x,t) + vcx(x,t) = 0 (1)
on an interval [0,2π] with v = 1, periodic boundary conditions and two different initial values c(x,0) = sin(x) (2)
and
c(x,0) =  
0 : x ≤ 1 3 1 : 1 3 < x < 2 3 0 : x ≥ 2 3
(3)
In both cases, run until time T = 4π when the solution should be identical again to the initial solution, because two full revolutions have been completed.
1. Implement the pseudo-spectral method with implicit midpoint rule to solve Equation (1). You may reuse the code that is available on Minerva.
2. Retrieve the first order upwind Finite Volume method with forward Euler for the transport equation from the VLE and set it up to solve the example described above.

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Tellus molestie nunc non blandit massa enim nec dui. Tellus molestie nunc non blandit massa enim nec dui. Ac tortor vitae purus faucibus ornare suspendisse sed nisi. Pharetra et ultrices neque ornare aenean euismod. Pretium viverra suspendisse potenti nullam ac tortor vitae. Morbi quis commodo odio aenean sed. At consectetur lorem donec massa sapien faucibus et. Nisi quis eleifend quam adipiscing vitae proin sagittis nisl rhoncus. Duis at tellus at urna condimentum mattis pellentesque. Vivamus at augue eget arcu dictum varius duis at. Justo donec enim diam vulputate ut. Blandit libero volutpat sed cras ornare arcu. Ac felis donec et odio pellentesque diam volutpat commodo. Convallis a cras semper auctor neque. Tempus iaculis urna id volutpat lacus. Tortor consequat id porta nibh.

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Question 1 : Caches are important to providing a high-performance memory hierarchy to processors. Below is a list of 32-bit memory address references, given as word addresses. 3, 180, 43, 2, 191, 88, 190, 14, 181, 44, 186, 253 a >>  For each of these references, identify the binary addres ...

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1. What can be said about the domain of the function f \circ g where f(y)= \frac{4}{y-2} and g(x)= \frac{5}{3x-1} ? Express it in terms of a union of intervals of real numbers. Go to www.desmos.com/calculator and obtain the graph of f , g , and f \circ g . 2. Find the inverse of the function f(x)=4+ ...

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Given vectors a = h−2,−1,0i, b = h3,1,−2i and c = h1,−2,2i a) Find the angle between a and b .b) Determine which (if any) of a , b and c are perpendicular to each other .c) Calculate the projection of b onto a−c . d) Find (b−a)×c .Question 2. 11+4=15 marks C ...

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Suppose you are on a platform 27m above the sea and toss a ball directly upwards at3.5m/s and allow it to fall into the sea.Some notesa general equation for rectilinear motion under constant acceleration (for example,in free fall) is s(t) = s0 +v0t+0:5at2 , where s is displacement or position (use u ...

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