Given the first-order ODE dx/dt= -700x - 1000e-1 x(t = 0) = 4 Solve this stiff differential

Question:

Given the first-order ODE

dx/dt= -700x - 1000e-1

x(t = 0) = 4

Solve this stiff differential equation using a numerical method over the time period 0 ≤ t ≤ 5. Also solve analytically and plot the analytic and numerical solution for both the fast transient and slow transition phase of the timescale.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Numerical Methods For Engineers

ISBN: 9780071244299

5th Edition

Authors: Steven C. Chapra, Raymond P. Canale

See More Books

Question Posted: Dec 13, 2011 10:11 AM

See More Questions

Solve the nondimensional transient heal conduction equation in two dimensions, which represents the transient temperature distribution in an insulated plate. The governing equation is 2u/x2 + 2u/y2 =...
For each DE in problems solve analytically to obtain solution curves through the point (1,1) and (-1,-1), Then using an appropriate software package draw the direction field and superimpose your...
Using the Laplace transform, solve the following differential equation for Subject to i(0) = 0,i(0) = 2 . di di
Complete the horizontal analysis of the following comparative income statement? Mile Wide Organic Woolens, Inc. Comparative Income Statement For Years Ending December 31, 2012 and 2013 Increase...
Gary Stevens, the newly hired manager of an engineering company, does not understand how the cost of the firm's equipment is expensed. In memo format, explain to him how depreciation provides a means...
Each of the graphs of the functions in Exercises has one relative maximum and one relative minimum point. Plot these two points and check the concavity there. Using only this information, sketch the...
Are there any other objectives you would have prioritised? (If so, which and why?)
The shares of Volkswagen trade on the Frankfurt stock exchange. A U.S. investor purchased 1,000 shares of Volkswagen at 56.91 each, when the exchange rate was :$ = 0.9790-0.9795. Three months later,...
Juniper Design Ltd. of Manchester, England, is a company specializing in providing design services to residential developers. Last year the company had net operating income of $420,000 on sales of...
What is the solution of the recursive equation T (n) = 0.015625T +n?? (1/4) a) O(n') b) O(n' lg n) c) O(n* Ign) d) O(7*)
Consider the thin rod of length l moving in the x - y plane as shown in Figure. The rod is fixed with a pin on one end and a mass at the other. Note that g = 9.8l m/s 2 and l = 0.5 m. This system can...
The following second-order ODE is considered to be stiff d2y/dx2= -l00l dy/dx - l000y Solve this differential equation (a) Analytically and (b) Numerically for x = 0 to 5. For (b) use an implicit...
Consider for a moment that the dust and gas reservoirs in the solar nebula both had oxygen isotope compositions at G in Figure 9.17. Where would the isotope compositions plot if we mixed small...
As of June 30, 2012, the bank statement showed an ending balance of $\$ 13,879.85$. The unadjusted Cash account balance was $\$ 13,483.75$. The following information is available: 1. Deposit in...
An engineering study has developed the following cost data for the production of product A: (1) If the current production level is 1,500 units, what is the incremental cost of producing an additional...
On December 1, a group of individuals formed a corporation to establish the Local, a neighborhood weekly newspaper featuring want ads of individuals and advertising of local firms. The free paper...
Design an arithmetic circuit with one selection variable S and two n-bit data inputs A and B. The circuit generates the following four arithmetic operations in conjunction with the input carry C in ....
For the system you chose for Problems and Exercises 3, complete section 4.0, A-C, Management Issues, of the BPP Report. Why might people sometimes feel that these additional steps in the project plan...
This is when work is assigned to workcenters based simply on when it is needed. Resources required to complete the work are not considered.WT-202
Wilsons Auto Repair ended 2011 with Accounts Receivable of $85,000 and a credit balance in Allowance for Uncollectible Accounts balance of $11,000. During 2012, Wilsons Auto Repair had the following...
Calcium metal and water produce hydrogen gas. If the volume of wet gas collected over water is 95.0 mL at 20 C and 758 mm Hg, what is the volume of dry gas at STP conditions? (The vapor pressure of...
Heat treating is often used to carburize metal parts, such as gears. The thickness of the carburized layer is considered a crucial feature of the gear and contributes to the overall reliability of...
Statistics for 21 National Hockey League teams were obtained from the Hockey Encyclopedia and are shown in Table 12-8. The variables and definitions are as follows: Wins Number of games won in a...
Consider the linear regression model where and where x1 = xi1/n and x2 = xi2/n. (a) Write out the least squares normal equations for this model. (b) Verify that the least squares estimate of the...
This is a partial adjusted trial batance of Cullumber Compary manualys
Which of the following journal entries will record the payment of a $1,500 salaries payable originally incurred for Salaries Expense? Select one: A. Debit Salaries Expense; credit Salaries Payable B....
What is the definition of substantially appreciated inventory? A. Inventory with a FMV greater than its basis B. Inventory and unrealized receivables with a FMV greater than their basis C. Inventory...

Given the first-order ODE dx/dt= -700x - 1000e-1 x(t = 0) = 4 Solve this stiff differential

Question:

Step by Step Answer:

Analytic solution Take Laplace transform Substituting the initial condition and expanding t...View the full answer

Numerical Methods For Engineers

Students also viewed these Numerical Analysis questions