Question

Please use Matlab to solve this problem

EECE 4694 Numerical Methods and Computer Applications Homework -5 1. A condenser of capacity C is discharged through an inductance L and a resistance R in series, and the chargc g at any timc t is given by at2 Given that L-10mH. R-200 ohms. C-0.1μF, and also when 1-0, charge q- 0.01coulomb, and current 0 i. Using finite difference methods for initial value problems, find the value of q from time t0 to t 50μ.sec, using a) n 10 steps, and b) n 100 steps. For both values of n compare your results (on the same plot) with the exact solution given below for the same conditions: ii. qe1000 0.01cos(30000t) 0.0033 sin(30000t)] 2. A non-insulated uniform rod positioned between two bodies of constant but different temperature is shown below. If Tu-20°Cis the temperature of the surrounding and α-0.01 m-2 is a heat cocfficient for the rate of heat dissipation to the surrounding, and where the temperatures at the ends of the bar are held at fixed values: T(0) = T1 = 40°C T(L) = T2 = 200°C i. Usc linite dilleren㏄ melhods for boundary value problems to solve for the len!peral ure lor u 10m rod with steps Ax - 2m if at a steady state the system can be represented by: a2r T. T. X=() ii. Compare your results (on the samc plot) with the exact solution given bclow for the samc conditions: T = 73.4523e0.1x-53.4523e-0.1x + 20 Use Least Squares methods with the following data. 10 25 15 32 20 25 38 30 36 35 39 40 40 45 42 50 16 i. Fit a straight line ii. Fit a sccond-order polynomial iit an exponential function Plot the data along with all the curves. Provide a table of all the data from the table and from the curves for the given values of x. Compute the mean square error for each curve. Is any of the curves superior? Why? Page 1 of 1

Answer 1

Gngid to lo dato 16 25 32 33 38 36 39 40 2 42 -Tha Valuos of 2x, cy.SX*, Edy ωんchaOQ : ag folloly 5 6 25 BO 2.5 too 85o 15 32 225u8 20 33 4oo 60 25 38 625 960 30 86 0 o80 3S 39 1285 1365 yo uo 600 600 45 2 2025 8fo 10,455

7x: 10 15 3 20 33 400 8000 160 000 25 lot looo 1o,oo aSo soo 215 3335 50,uB000 660 132oo 950 83,75 o loso 3a,uoo 25 33 62s 156a3 30 625 1030 3 36 36 oo a 000 310,0o0 35 39 as a835 150o 635 1365 u,25 49 42 2025 ,185 0065 1840 85,050 5o 42 2500 1a5,000 6250000 loo loo m-1o -6,2รา.333, at-580.4366 a2 10.0545

7x: 10 15 3 20 33 400 8000 160 000 25 lot looo 1o,oo aSo soo 215 3335 50,uB000 660 132oo 950 83,75 o loso 3a,uoo 25 33 62s 156a3 30 625 1030 3 36 36 oo a 000 310,0o0 35 39 as a835 150o 635 1365 u,25 49 42 2025 ,185 0065 1840 85,050 5o 42 2500 1a5,000 6250000 loo loo m-1o -6,2รา.333, at-580.4366 a2 10.0545

Apply n on B- A-7986 as 131863 Loo 32- 18 9 Lo 2s 3a13 5 323465 aas 51 9861 20 333.4965 yoo 69.9302 6as o.9H 33 36376 30 36 3S8352 5 39 36636 y6 O 3.6889 aas a3.8a 6 16oo u.556 202s 168 19515 so u2 3737672500 186 8335

A 3.0376 b o.O16824 lna 3. 6376 ae3 0376 6-3551 3 (o-O16824)乂
hope you understand thank you