dy dt using the Euler method with ?t\'. 0.18 and initial guess: y() time step of

Question

dy dt using the Euler method with ?t'. 0.18 and initial guess: y() time step of At2 0.05s and carry out the calculation again with a 18. The re-arrangement of the problem so that it can be solved by standard methods is dt (c) dy-+5 (d) d+2t -Sy (e) none of the above 19. report the solution at t-. 0.18 using the ?t1-0.1 s time step. (d) y(0.1) 1.558 (e) none of the above 20. report the solution at t 0.1 s using the ?, = 0.05s time step (b) y(0.1)=1.767 (c) y(0.1) 1.693 () y(0.1)-1.558 (e) none of the above 21. report an error estimate for the solution using the 0.1s time step. (a) error 4.1 x 10-1 (b) error= 1.5×10-2 (c) error 1.8 x 10-1 error1.3 x 10 none of the above (e)

Explanation / Answer

18)

dy/dt = 5y - 2t

so B

19)

y(0) = 0

so y'(0) =0
so y(0.1) = y(0) + 0.1*y'(0) = 0 + 0.1*0 = 0

so E

20)

y(0.05) = 0 + 0.05*0 = 0

so dy/dt = 5*0 -2*0.05 = -0.1

so y(0.1) = 0 + 0.05*-0.1 = -0.005

so E

21)

Error =1.5 * 10-1

So B

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