Tutorial_12.pdf - ESO 208A Computational Methods in Engineering Tutorial 12 Ordinary Differential Equations Initial Value Problems(IVPs 1 Solve the

Tutorial_12.pdf - ESO 208A Computational Methods in...

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ESO 208A: Computational Methods in Engineering Tutorial 12 Ordinary Differential Equations: Initial Value Problems (IVPs) 1. Solve the differential equation y y x dx dy 2 2 with y (0) = 1 and h = 0.1, over the interval 1 , 0 x using the following methods: (a) Euler Forward (b) Euler Backward (c) Trapezoidal (d) 2nd Order Runge-Kutta (e) Solve analytically and compare (i) the solutions graphically with the analytical solution and, (ii) numerically the true relative errors of the above methods at every time step. 2. Consider a LR -circuit with a resistance ( R ) and an inductance ( L ). A time varying potential of E ( t ) is applied to the circuit. Application of Kirchoff’s law leads to the following differential equation for the current ( i ):   t E Ri dt di L Compute the current at every 0.2 hours for 3 hours due to application of a square voltage   0 0 24 0 1 0 1 t E t t t Given are the values of inductance L = 12 H and the resistance R = 18 . The initial condition is i = 0 at t = 0. Solve using 4th order Adam’s Moulton, 4 th
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