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IN PYTHON: 6. Stiff Problem Consider the initial value problem y = -500(y - cost) -...
3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find the first-order correction, y (t), for the initial value problem with є * 0 and є is a small parameter. 3. Consider the initial value problem dt Solve the initial value problem for є = 0, to obtain y(t) 3e-21 Using the method of perturbations, setting y-Yo + єу, find...
Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1, y"(0)-0. rect? Solve the following initial value problem using ode45 and ode15s: y",(t) _ Зу"(t) + ty(t) _ sin2(t)-7, o s t Plot the solution for varying tolerances. Why do you believe your solution is cor- 2. 1, y(0)-0, y,(0) 1,...
[7] 1. Consider the initial value problem (IVP) y′(t) = −y(t), y(0) = 1 The solution to this IVP is y(t) = e−t [1] i) Implement Euler’s method and generate an approximate solution of this IVP over the interval [0,2], using stepsize h = 0.1. (The Google sheet posted on LEARN is set up to carry out precisely this task.) Report the resulting approximation of the value y(2). [1] ii) Repeat part (ii), but use stepsize h = 0.05. Describe...
3. Consider the initial value problem y(t) = y, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method 9n+1 := yn + hf(en +3.29 + s(tn, yn)), for this initial value problem. c. What is the difference between the two...
Problem 2. (a) Solve the initial value problem I y' + 2y = g(t), 1 y(0) = 0, where where | 1 if t < 1, g(t) = { 10 if t > 1 (t) = { for all t. Is this solution unique for all time? Is it unique for any time? Does this contradict the existence and uniqueness theorem? Explain. (b) If the initial condition y(0) = 0 were replaced with y(1) = 0, would there necessarily be...
3. Consider the initial value problem y'(t) = y2, y(0) = 1. a. Write down (i.e., write the formula which describes one step, Yn+1 = yn + ...) the second order Taylor method with step size h for this initial value problem. b. Write down the time stepping formula Yn+1 = Yn +... for the modified Euler method h Yn+1 := yn + hf(tn + h 2:9 » Yn + 5 f (tnYn)), for this initial value problem. c. What...
Assume that y' = y.t needs to solved i.e.one needs to find y(t) for the initial condition yo = 0.3. In your Math classes, you were taught how to solve this differential equation. However, most differential equations are not easily solvable, and one needs to resort to numerical integration. This can easily be done in MATLAB for explicit first order differential equations like the one stated above. The time of interest is between tstart <t <tend let's say between O...
Consider the initial value problem for function y given by, Consider the initial value problem for function y given by, (a) Find the Laplace Transform of the source function, F(s) = L[-3 F(s) = (b) Find the Laplace Transform of the solution, Y(s) Lt) Y(s) - (c) Find the solution y(t) of the initial value problem above. s(t) Recall: If needed, the step function at c is denoted as u(t - c) -1] Help Entering Answers Preview My Anawers Submit...
[15] 9. By using the Laplace transform method solve the initial value problem Y" + 2y + y = sint, y(0) = 0, y(0) = 0.
14. Consider the initial value problem where y is the damping coeficient (or resistance). (a) Let γ =-. Find the solution of the initial value problem and plot its graph. (b) Find the time t, at which the solution attains its maxi mum value. Also find the maximum value y, of the solution. (c) Let γ = 4 and repeat parts (a) and (b). (d) Determine how ti andy, vary as γ decreases. What are the values of, and y,...