Question: Consider the differential equation dy dt + 2y = e t , y(0) = 1. a. Calculate the exact solution y(2). b. Now use Eulers

Consider the differential equation dy dt

+ 2y = e t

, y(0) = 1.

a. Calculate the exact solution y(2).

b. Now use Euler’s method to calculate approximate values of y(2) using h = 1.0, 0.5, 0.25, 0.125 and h = 0.0625.

Don’t do this by hand! Use a computer.

c. Calculate the error (i.e., the difference between the approximate value and the true value) for each value of h.

d. Plot the absolute value of the error against h. What do you notice about how the error depends on h?

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Modern Mathematical Statistics With Applications Questions!

Q:

Please solve this by using Matlab dt = dt Q2. The Explicit Euler Formula: Let as(+) = F(t, $(t)) be an explicitly defined first order ODE with interval (to, ty] with spacing h. Without loss of...

Q:

3. 8 E\\oints total] "This problem involves sofving the ordinary differential equation: dy a Y subject to y(0) =2 a. [2 points] Starting from # = 0, Use Euler's method with 4 = 0.2 and find the...

Q:

11. (5 points each, 20 points in all) Consider the logistic differential equation dy dt = $ (6 - y). Let y = f(t) be the particular solution to the differential equation with f (0) = 8. (a) What is...

Q:

Let's do one together first: the langer Consider the differential equation -dy = e (3x - 6x). Let y = f(x) be the particular solution to the differential equation that passes through (1, 0). (a)...

Q:

Consider the differential equation dy = 4x, with initial condition y (0) = 2. A. Use Euler's method with two steps to estimate y when c = 1: y(1) ~ (Be sure not to round your calculations at each...

Q:

Name Student ID Final MAT 22B, Friday August 4, 2017 Instructions: This exam is closed notes, closed books, no calculators and no electronic devices of any kind. There are five problems worth 35...

Q:

Final Review Set (Summer 2017)- Math 246 Show all your work for each problem 1) [6] (a) Use Euler's Method to approximate the solution to x '(t) = 1+ t sin(tx), x(0) = 0 at t=1 using eight steps. (b)...

Q:

I'd like the solution to the third part if all of it isn't possible :) clear a = 0; % start time b = 200; % end time e = 0.6; % initial conditions q10=1-e; % given q20=0; % given p10=0; % given...

Q:

1) [8] (2) Use Euler's Method to approximate the solution to I'(!) = 1+ isin(ux), x(0) =0 at +=1 using ten steps. (b) Do the same with the improved Euler method and compare results. 1) [7] Solve the...

Q:

***SCROLL DOWN**** This is definitely a longer homework question but I have no idea how to even start answering it. I have it attached below, and I would really appreciate to whoever helps answer...

Q:

Different airlines depreciate the same airplanes but using different useful-life and residual value assumptions. For example, airlines have depreciated the same Boeing aircraft over lives ranging...

Q:

Given $100,000 to invest, construct a value-weighted portfolio of the four stocks listedbelow Number of Shares Outstanding (millions) Price/Share ($) 13 Stock Golden Seas Jacobs and Jacobs MAG PDJB...

Q:

Preferred stock may be good for a company because it: Multiple Choice expands the capital base of the firm without diluting the common stock ownership. does not require interest payment in times of...

Q:

A friend taking calculus is puzzled. She remembers that for a function of one variable, if the first derivative is zero at a point and the second derivative is positive, then there must be a relative...

Q:

15.62 Consider the one-way analysis of variance setup. a. Show that the within-groups sum of squares can be written as follows: SSW = a K i=1 a ni j=1 x2 ij - a K i=1 nix2 i b. Show that the...

Q:

15.63 Consider the two-way analysis of variance setup, with one observation per cell. a. Show that the between-groups sum of squares can be written as follows: SSG = H a K i=1 x2i ~ - nx2 b. Show...

Q:

15.64 A delivery company manager needs information on the mean delivery time (in minutes) for five different locations in Sichuan, ChinaChengdu, Leshan City, Garze, Jiuzhaigou County, and Daocheng...

Q:

Effect of transactions on cash flows State the effect (cash receipt or cash payment and amount) of each of the following transactions, considered individually, on cash flows: a. Retired $270,000 of...

Q:

Based on the information shown below, what is the taxable profit for the period? Accounting profit before income tax Fines and penalties (non-deductible) Depreciation of plant (accounting)...

Q:

Exercise 9-13A (Algo) Ratio analysis LO 9-2, 9-3, 9-4, 9-5 Following is the balance sheet of Thornton Company for Year 3: Assets. Cash THORNTON COMPANY Balance sheet Marketable securities Accounts...