Question

Solve numerically the ODE,d(y)/(d)t=2t-ty for the interval tin[-1,3] using the third-order RungeKutta method given in the course notes. Use a step size of 0.5 . The initial condition is given as y(-1)=0. The exact (true) solution is given as y_(e)(t)=2-2e^((1-x^(2))/(2)). Display your results in tabulated form as shown below where at time t=t_(i),y_(i) represents the numerically estimated value of y,y_(e_(i)) represents the true value of y and |\epsi _(t)| is the corresponding true percent absolute relative error. \table[[i,t_(i),y_(i),y_(e_(i)),|\epsi _(t)|

Name: solve numerically the odedydt2t ty for the interval tin 13 using the third order rungekutta method given in the course notes use a step size of 05 the initial condition is given as y 10 the 95638
Uploaded: 2023-06-26T01:31:04-08:00
Duration: 6 min 16 s
Channel: Madhur L
Description: solve numerically the odedydt2t ty for the interval tin 13 using the third order rungekutta method given in the course notes use a step size of 05 the initial condition is given as y 10 the 95638

          Solve numerically the ODE,d(y)/(d)t=2t-ty for the interval tin[-1,3] using the third-order RungeKutta method given in the course notes. Use a step size of 0.5 . The initial condition is given as y(-1)=0. The exact (true) solution is given as y_(e)(t)=2-2e^((1-x^(2))/(2)). Display your results in tabulated form as shown below where at time t=t_(i),y_(i) represents the numerically estimated value of y,y_(e_(i)) represents the true value of y and |\epsi _(t)| is the corresponding true percent absolute relative error.
\table[[i,t_(i),y_(i),y_(e_(i)),|\epsi _(t)|

solve numerically the odedydt2t ty for the interval tin 13 using the third order rungekutta method given in the course notes use a step size of 05 the initial condition is given as y 10 the 95638

Added by Angela B.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Madhur L

06/26/2023

Step 1

Use a step size of 0.5. The initial condition is given as $y(-1) = 0$. The exact (true) solution is given as $y_e(t) = 2 - 2e^{(1-x^2)/2}$. Display your results in tabulated form as shown below where at time $t = t_i$, $y_i$ represents the numerically estimated Show more…

Show all steps

Thanks for your feedback!

Solve numerically the ODE,d(y)/(d)t=2t-ty for the interval tin[-1,3] using the third-order RungeKutta method given in the course notes. Use a step size of 0.5 . The initial condition is given as y(-1)=0. The exact (true) solution is given as y_(e)(t)=2-2e^((1-x^(2))/(2)). Display your results in tabulated form as shown below where at time t=t_(i),y_(i) represents the numerically estimated value of y,y_(e_(i)) represents the true value of y and |\epsi _(t)| is the corresponding true percent absolute relative error. \table[[i,t_(i),y_(i),y_(e_(i)),|\epsi _(t)|