psheet3 - Data Analysis Modelling and Simulation MATH1711...

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Data Analysis Modelling and Simulation MATH1711 Epiphany Term Practical Sheet 3 Aim : Two methodologies for solving difference equations (rsolve http://fife.dur.ac.uk:8080/AiM/. Further, you will numerically compute the region of stability for second-order difference equa- tions. Do not start the third sheet until you have finished the second – also note the “Hint” at the bottom of the second page . The “Flower” example with various parameters Solve the recurrence relations (a) y n +2 = 3 y n +1 - 2 y n , y 0 = 0, y 1 = 3; (b) y n +2 = 4 y n +1 - 4 y n , y 0 = 1, y 1 = 4; (c) y n +2 = y n +1 - y n , y 0 = 0, y 1 = 1. Revisiting the signal processing example (linearity) Solve the first-order difference equation y n +1 = ay n + x n , y 0 = 0 (a) Taking x n = ( - 1) n / 10, then x n = cos( nπ/ 100). What answer do you get with x n = ( - 1) n / 10 + cos( nπ/ 100)? (b) Change the initial condition to y
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psheet3 - Data Analysis Modelling and Simulation MATH1711...

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