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Question 20 1 pts Problem 20: Numerical solution of Ordinary differential equations Consider the following initial...
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial...
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial value problem GE:+15y = 1.C:y(0) -0.5 Carry out two-steps of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.1. and the predicted solutions is y(0.2)-0.20 None of the above. y(0.2) - -0.75 y(0.2)-1.27 y(0.2)=0.25
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial...
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial...
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
( x Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the...
( x Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: +15y = t 1.C:y(0) = 0.5 Using Euler's method, and a time step of At 0.2. do you expect the numerical solution not to oscillate and to be stable? None of the above. No, because Euler's method is implicit and there is not stability limit on At. Yes, because Euler's method is explicit and there is not stability limit...
Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial...
Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = + 1.C: y(0) 0.5 Using Euler's method, and a time step of At = 0.2. do you expect the numerical solution not to oscillate and to be stable? No, because the time step far exceeds the critical value At stable < 0.067 for this problem. None of the above Yes, because Euler's method is explicit and there is...
Consider the following ordinary differential equation: y' - sin(4t) = 0 (Eq. 4) The boundary condition...
Consider the following ordinary differential equation: y' - sin(4t) = 0 (Eq. 4) The boundary condition is that y(0) = -0.25. When the position y is a function of time, t, this describes an oscillating system – it's an example of simple harmonic motion. Functions like this are extremely common when considering mechanical systems. Write MATLAB code to carry out the following tasks: a) Apply the Taylor method for solving this equation (up to t4) for 20 steps, using a...
Need Help with solving for answers in Part C and Part D! Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0,3, and 0.4, (A COmputer algebra system is recomm...
Need Help with solving for answers in Part C and Part D!
Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0,3, and 0.4, (A COmputer algebra system is recommended. Round your answers to five decimal places.) (a) Use the Euler method with0.05 (0.11.5875 y(0.2)2.12747 y(0.3)2.62455 y(0.4)3.0829 (b) Use the Euler method with h0.025 y(0.1)1.58156 y(0.2)2.11675 (o.3)261 y(0.4)3.0654 (c) Use the backward Euler method with h 0.05 (0.2) y(0.3) y(0.4) (d) Use...
equations Ordinary Differential Homework problem 8 consider the initial value problem So if ostki - by...
equations Ordinary Differential Homework problem 8 consider the initial value problem So if ostki - by Ist 25 12 If if 5< t < ycod=4 your solve for equation for Y Y=[{y} = on both sides of the Take invertse laplace transform previous equation to sclue for y y =
Consider the initial value problem below to answer to following. a) Find the approximations to y(0.2)...
Consider the initial value problem below to answer to following. a) Find the approximations to y(0.2) and y(0.4) using Euler's method with time steps of At 0.2, 0.1, 0.05, and 0.025 b) Using the exact solution given, compute the errors in the Euler approximations at t 0.2 and t 0.4. c) Which time step results in the more accurate approximation? Explain your observations. d) In general, how does halving the time step affect the error at t 0.2 and t...
Hello! I need help with this college level differential equations question. Please show work and ...
Hello! I need help with this
college level differential equations question. Please show work and
thank you.
3. Consider the initial value problem y' (t) 1 0y(t) y(0) Clearly, the solution to the system is y(t) = et and 2(t) = e-10 t. Suppose we tried solving the system using forward Euler. This would give us with to 0, y(to) 1, and z(to-1. a. Show that the numerical solution for z(t) will only tend to zero if Δι < 2...
Question 22 1 pts Problem 22: Numerical solution of Ordinary differential equations Consider the following initial value problem GE:+15y = 1.C:y(0) -0.5 Carry out two-steps of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.1. and the predicted solutions is y(0.2)-0.20 None of the above. y(0.2) - -0.75 y(0.2)-1.27 y(0.2)=0.25
Question 21 1 pts Problem 21: Numerical solution of Ordinary differential equations Consider the following initial value problem G.EE +15y = 1.C:y(0) - 0.5 Carry out a single step of the modified Euler (trapezoidal) method solution from the initial condition with a time step of At = 0.2, and the predicted solutions is Y(0.2)-0.20 None of the above y(0.2)-1.27 Y(0.2)-0.25 (0.2)--0.75
Question 23 1 pts Problem 23: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = 1.C:y(0) = 0.5 Using the results in question 21 and 22, the computed absolute value of the error estimate e for the modified Euler predicted solution using a time step of At = 0.2.is None of the above. Ec-0.12 Ec-0.42 Ec-1.42 Ec-15.42 21 Y(0.2) = 0.5 +0.77=1.27 k, = 0.2 [0.15 (0.5))=-1.5 K2=0.2 [02-151-1)] = 3.04 k=kitky =...
( x Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: +15y = t 1.C:y(0) = 0.5 Using Euler's method, and a time step of At 0.2. do you expect the numerical solution not to oscillate and to be stable? None of the above. No, because Euler's method is implicit and there is not stability limit on At. Yes, because Euler's method is explicit and there is not stability limit...
Question 19 1 pts Problem 19: Numerical solution of Ordinary differential equations Consider the following initial value problem GE: + 15y = + 1.C: y(0) 0.5 Using Euler's method, and a time step of At = 0.2. do you expect the numerical solution not to oscillate and to be stable? No, because the time step far exceeds the critical value At stable < 0.067 for this problem. None of the above Yes, because Euler's method is explicit and there is...
Consider the following ordinary differential equation: y' - sin(4t) = 0 (Eq. 4) The boundary condition is that y(0) = -0.25. When the position y is a function of time, t, this describes an oscillating system – it's an example of simple harmonic motion. Functions like this are extremely common when considering mechanical systems. Write MATLAB code to carry out the following tasks: a) Apply the Taylor method for solving this equation (up to t4) for 20 steps, using a...
Need Help with solving for answers in Part C and Part D!
Find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0,3, and 0.4, (A COmputer algebra system is recommended. Round your answers to five decimal places.) (a) Use the Euler method with0.05 (0.11.5875 y(0.2)2.12747 y(0.3)2.62455 y(0.4)3.0829 (b) Use the Euler method with h0.025 y(0.1)1.58156 y(0.2)2.11675 (o.3)261 y(0.4)3.0654 (c) Use the backward Euler method with h 0.05 (0.2) y(0.3) y(0.4) (d) Use...
equations Ordinary Differential Homework problem 8 consider the initial value problem So if ostki - by Ist 25 12 If if 5< t < ycod=4 your solve for equation for Y Y=[{y} = on both sides of the Take invertse laplace transform previous equation to sclue for y y =
Consider the initial value problem below to answer to following. a) Find the approximations to y(0.2) and y(0.4) using Euler's method with time steps of At 0.2, 0.1, 0.05, and 0.025 b) Using the exact solution given, compute the errors in the Euler approximations at t 0.2 and t 0.4. c) Which time step results in the more accurate approximation? Explain your observations. d) In general, how does halving the time step affect the error at t 0.2 and t...
Hello! I need help with this
college level differential equations question. Please show work and
thank you.
3. Consider the initial value problem y' (t) 1 0y(t) y(0) Clearly, the solution to the system is y(t) = et and 2(t) = e-10 t. Suppose we tried solving the system using forward Euler. This would give us with to 0, y(to) 1, and z(to-1. a. Show that the numerical solution for z(t) will only tend to zero if Δι < 2...
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