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3.) (1 point) Revisit our example from class and estimate y(O) for the ODE: y'= y...
Answer why the approximations are so inaccurate for this particular value of the stepsize. Consider the IVP -2.9y, (0) 2 for 0 sts1 The exact solution of this IVP is y-2e-291 The goal of this exercise is to visualize how Euler's method is related to the slope field of the differ ential equaton. In order to do this we will plot the direction field together with the approximations and the exact solution (c) Enter the function defining the ODE as...
2. Consider the following first-order ODE from x = 0 to x = 2.4 with y(0) = 2. (a) solving with Euler's explicit method using h=0.6 (b) solving with midpoint method using h= 0.6 (c) solving with classical fourth-order Runge-Kutta method using h = 0.6. Plot the x-y curve according to your solution for both (a) and (b).
Consider the ODE f(x,y) = - 10r5 Take initial conditions xo = 0 , yo = y(0) = 11 , x1 = 0.2 and y y(0.2)= 22, solve for y(99) with a step size of 0.2 using an adaptation of Euler's method, which uses two known y solutions to approximate the next y solution. The general formula is: 3 Vi+2 i+1+ h 1 (owsan-cuea An example of the first few iterations is shown below. (wcomnce) (ceny5-cesn) y2 yh 3 (esa-c)...
using matlab thank you 3 MARKS QUESTION 3 Background The van der Pol equation is a 2nd-order ODE that describes self-sustaining oscillations in which energy is withdrawn from large oscillations and fed into the small oscillations. This equation typically models electronic circuits containing vacuum tubes. The van der Pol equation is: dt2 dt where y represents the position coordinate, t is time, and u is a damping coefficient The 2nd-order ODE can be solved as a set of 1st-order ODEs,...
need help with #2 & #3 January 19, 2018 This homeworksheet is due in class on Wednesday, January 24. The problems are similar to problems from your textbook Question: 23 Points: Score: 4 4 24 16 oximate the solution to the given 1. (16 points) Use Euler's Method with the given step size Ar to appr initial value problem. Your answer should have a table with approximate outputs at each step. (a) 2)0 + 7), y(O) 3.5, Ar 0.5. Approximate...
4. * Using your calculations from 3., plot the exact solution to dy = 1-y, dt y(0) = 1/2, for 0 <ts1, along with the numerical solution given by Euler's method and the trapezoid method, both with stepsize h = 0.1. Give the approximation of y(t = 1) for each numerical method. To distinguish your solutions: (i) Plot the Euler solution using crosses; do not join them with line segments. (ii) Plot the trapezoid solution using squares; again do not...
The phase plot for an ODE dy dx =f(y) dydx=f(y) is shown below. 4 3 2 1 2 1 1 1 1 2 3 (a) Which of these could be a plot of solutions y vs x corresponding to this ODE? 9 2 B. A. 2 2 3 C. D. You can click the graphs above to enlarge them. OA. A ов, в OC. C OD. D E which is choose (b) The smallest equilibrium of this ODE is y-...
Please answer ALL parts of the question. Will rate immediately!! Thank you!! 3. Modeling with Differential Equations a. Provide slope fields for the following differential equations: DE#1: y'-y-cos x; DE#3: y'-y-cos y. (4pts) DE#2: y-x-cos y, b. For each slope field, draw the solution curve for the initial condition y(0) 1. (4pts) Attach separate pages c. Use Euler's method to estimate y(2), using steps of h 0.5 and h0.1 '-y cosx,y(0)-1 You can use technology. Write your results accurate to...
Use Euler's method with step size 0.2 to estimate y(1), where y(x) is the solution of the initial-value problem y'=2x+y^2, y(0)=−1. y(1)= .
3. Euler's Method (a) Use Euler's Method with step size At = 1 to approximate values of y(2),3(3), 3(1) for the function y(t) that is a solution to the initial value problem y = 12 - y(1) = 3 (b) Use Euler's Method with step size At = 1/2 to approximate y(6) for the function y(t) that is a solution to the initial value problem y = 4y (3) (c) Use Euler's Method with step size At = 1 to...