Problem Thre: 125 points) Consider the following initial value problem: dy-2y+ t The y(0) -1 ea dt ical solution of the differential equation is: y(O)(2-2t+3e-2+1)y fr exoc the differential equat...
6. The differential equation: y 4y 2x y(0) 1/16 has the exact solution given by the following equation: v = (1 /2)s, + (14)s +1.16 Calculate y (2.0) using a step size h-0.5 using the following methods: (a) Euler (b) Euler P-c (c)4h order Runge-Kutta (d) Compare the errors for each method. (e) Solve using Matlab's ode45.m function. Include your code and a print of the solution.
The differential equation : dy/dx = 2x -3y , has the initial conditions that y = 2 , at x = 0 Obtain a numerical solution for the differential equation, correct to 6 decimal place , using , The Euler-Cauchy method The Runge-Kutta method in the range x = 0 (0.2) 1.0
Complete using MatLab 1. Consider the following initial value problem 3t2-y, y(0) = 1 Using Euler's Method and the second order Runge-Kutta method, for t E [0, 1] with a step size of h 0.05, approximate the solution to the initial value problem. Plot the true solution and the approximate solutions on the same figure. Be sure to label your axis and include an a. appropriate legend b. Verify that the analytic solution to the differential equation is given by...
Consider the following initial value problem у(0) — 0. у%3D х+ у, (i) Solve the differential equation above in tabular form with h= 0.2 to approximate the solution at x=1 by using Euler's method. Give your answer accurate to 4 decimal places. Given the exact solution of the differential equation above is y= e-x-1. Calculate (ii) all the error and percentage of relative error between the exact and the approximate y values for each of values in (i) 0.2 0.4...
2. (10 points) Consider the initial value problem y = y-2. and y(1) = 0. (a) (4 points) Use Euler's method with step size 0.5 to approximate y(2) (i.e., the value of y when x = 2)? (b) (6 points) Solve the differential equation (with the specified initial value) to get y as a function of r.
Assignment 2 Q.1 Find the numerical solution of system of differential equation y" =t+2y + y', y(0)=0, at x = 0.2 and step length h=0.2 by Modified Euler method y'0)=1 Q.2. Write the formula of the PDE Uxx + 3y = x + 4 by finite difference Method . Q.3. Solve the initial value problem by Runga - Kutta method (order 4): y" + y' – 6y = sinx ; y(0) = 1 ; y'(0) = 0 at x =...
Matlab & Differential Equations Help Needed I need help with this Matlab project for differential equations. I've got 0 experience with Matlab other than a much easier project I did in another class a few semesters ago. All we've been given is this piece of paper and some sample code. I don't even know how to begin to approach this. I don't know how to use Matlab at all and I barely can do this material. Here's the handout: Here's...
2. Coupled Differential Equations (40 points) The well-known van der Pol oscillator is the second-order nonlinear differential equation shown below: + au dt 0. di The solution of this equation exhibits stable oscillatory behavior. Van der Pol realized the parallel between the oscillations generated by this equation and certain biological rhythms, such as the heartbeat, and proposed this as a model of an oscillatory cardiac pacemaker. Solve the van der Pol equation using Second-order Runge Kutta Heun's method with the...
[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...
1. Consider the differential equation dy/dt = 0.2y(t) -2, y(0) = 40. (a) Showing your work, calculate y(0.2) using Euler's Method and a step size of At = 0.1 (b) Repeat with At = 0.2 and compare your answer with (a) 2. Consider the number of phone calls in a minute to a corporate Delta Airlines (800) number is Poisson distributed with a mean of 1. = 7.5 during the busy hour. (a) What is the probability of no calls...