ATLAB BUILT CODE REQUEST FOR 4 QUESTION.

Computer Networking: A Top-Down Approach (7th Edition)
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Chapter1: Computer Networks And The Internet
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MATLAB BUILT CODE REQUEST FOR 4 QUESTION. 

 

Q4. Solve the above equations using Runge-Kutta 2nd-order method in the Matlab.
Q5. Also, solve this problem using Euler's method in Matlab.
Q6. Similar to the requirements in Q3, plot the velocities by using the methods in Q4 and Q5.
And then discuss the similarities and differences by comparing 3 different methods that you
used to solve the problem above, and in the end make a conclusion which one is the best
method based on your own analysis and understanding.
Reference:
Definition of Runge-Kutta 4-order method for 2nd order ODE:
dx
dt
d²x
dt² =f(t, x, v),
=v, x(₂)=xo. v(1₂) = Vo
²₁+₁=4₁+h₂
h = stepsize
dx₂ = hxv₂
dv₂ = kxf (₁,₁,₂)
_dx;= h (v₁ + ½dv₁)
dv₂ = kxf (t; + ½h.x; + ½ dx;,v; +{dv₂)
dx₂ = h (v₁ + dv₂)
dv₂ = kxf (t; + ½ h‚x, + ½dx₂,v,+ dv₂)
dx₂ =h(v₁ + dv₂)
dv₂ = hxf(t₁ +h₂x₁ + x₂v₂ + dv₂)
X1+₁ = x₁ + ² (dx₂ + 2dx₂ + 2dx, +dx₂)
= v₁ + ² (dv₂ + 2dv₂ + 2dv¸ + dv₂)
Transcribed Image Text:Q4. Solve the above equations using Runge-Kutta 2nd-order method in the Matlab. Q5. Also, solve this problem using Euler's method in Matlab. Q6. Similar to the requirements in Q3, plot the velocities by using the methods in Q4 and Q5. And then discuss the similarities and differences by comparing 3 different methods that you used to solve the problem above, and in the end make a conclusion which one is the best method based on your own analysis and understanding. Reference: Definition of Runge-Kutta 4-order method for 2nd order ODE: dx dt d²x dt² =f(t, x, v), =v, x(₂)=xo. v(1₂) = Vo ²₁+₁=4₁+h₂ h = stepsize dx₂ = hxv₂ dv₂ = kxf (₁,₁,₂) _dx;= h (v₁ + ½dv₁) dv₂ = kxf (t; + ½h.x; + ½ dx;,v; +{dv₂) dx₂ = h (v₁ + dv₂) dv₂ = kxf (t; + ½ h‚x, + ½dx₂,v,+ dv₂) dx₂ =h(v₁ + dv₂) dv₂ = hxf(t₁ +h₂x₁ + x₂v₂ + dv₂) X1+₁ = x₁ + ² (dx₂ + 2dx₂ + 2dx, +dx₂) = v₁ + ² (dv₂ + 2dv₂ + 2dv¸ + dv₂)
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