Question: Consider the backward difference method for solving the heat equation ut = Uxx un+1 2u7+1 h k LTE un = n+1 Ui+l where k

Consider the backward difference method for solving the heat equation ut = Uxx un+1 2u7+1 h k LTE un = n+1

Consider the backward difference method for solving the heat equation ut = Uxx un+1 2u7+1 h k LTE un = n+1 Ui+l where k is the time step and h is the grid spacing. The local truncation error, denoted by LTE, of this method is given by the equation n+1 + U-1 u(i,n+1) u(i,n) (i+1, n+1) 2u(2i,n+1)+u(2i-1,n+1) k 1 h (1) where u(x, t) denotes the exact solution to the heat equation. Using equation (1), write down an expression for the local truncation error. What is the order of accuracy of this method?

Step by Step Solution

★★★★★

3.45 Rating (148 Votes )

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 Accounting Questions!

Explain how the time value of money concept is incorporated into the valuation of long-term leases.

This problem combines equilibrium analysis with some of the things you learned in the chapter on intertemporal choice. It concerns the economics of saving and the life cycle on an imaginary planet...

The (m 1) (m 1) tridiagonal matrix is involved in the Backward Difference method to solve the heat equation. For the stability of the method we need (A1) a. = 1 / 4 b. = 1 / 2 c. = 3/4 When is...

It is a slow day at Bunsen Motors, so since he has his calculator warmed up, Clarence Bunsen (whose preferences toward risk were described in the last problem) decides to study his expected utility...

Task 3 (Processing encoder output) The data will be collected from the actual de motor system shown in Figure 2. The file contains data points of the time in msec versus the angular displacement in...

Use MATLAB to code this question 1. Use the finite difference method to solve the heat equation: u(z,0) = g(x), a

(a) Write a function function[u, T] = BackEuler (f, df, a, b, N, ya, maxiter, tol) that implements the Backward Euler method for a scalar differential equation y'(t) = f(t, y). Here, N is the number...

5. Illustrate the finite difference method for solving the two-point boundary value problem u" = u 3t ,0

Like the Heat equation, non-steady state mass transfer equation which is also a parabolic equation can be used to estimate the concentration of a pollutant in a river. (Please complete all parts and...

Problem One: (Based on Chapra. Problem 1.17. Page 22 According to Newton's law of cooling, the temperature of a body changes at a rate proportional to the difference between its temperature and that...

Problem Three: Based on Problem 1.17. Page 22. Chapra Textbook) According to Newton's law of cooling, the temperature of a body changes at a rate proportional to the difference between its...

Five companies bidded for 3 government projects. A company can be awarded only 1 project. Bids of companies for the projects are given in following tableau (in Million dollars). Objective of the...

Why do technical assistance programs by more affluent nations typically ignore the distribution problem or relegate it to a minor role in development planning? Explain.

E5.19 A second-order system has the closed-loop transfer function (a) Estimate the percent overshoot P.O., the time to peak Tp, and the settling time Ts of the unit step response. (b) Obtain the...

1. Write the equation for the titration of Ca2 + with EDTA. 2. Write the equations for the endpoint color change of Eriochrome Black T (EBT) with Mg2 + . 3. Report the water hardness as ppm CaCO3 of...

Using the following system of ODES (first order ODE set). xi = x2 x2 = -2 cos(t) - 4 cos(2t) How do you identify the initial condition for each equation? How do you apply Euler's method with four...

Draw it with a flow chart and briefly describe the isolation method that can be used to separate natural products that are semipolar from the leaves of a plant drug!

The Americans with Disabilities Amendments Act of 2008 emphasizes that the definition of disabilities should be construed broadly and should not require extensive examination.Group of answer...

Noting from Figure 13.16 that gas emissivity can be increased by adding water vapor, it is proposed to enhance heat transfer by injecting saturated steam at 100C at the entrance of the pipe of...

Derive the expression for the modified effectiveness*, given in Comment 4 of Example 11.8. Example 11.8 Spherical steel balls of diameter D = 10 mm are cooled from an initial temperature of Thi =...

Consider the situation of Problem 10.67 at relatively high vapor velocities, with a fluid mass flow rate of m = 2.5 kg/s. (a) Determine the heat transfer coefficient and condensation rate per unit...

The Energy Information Administration published a press release on September 26, 2005 (Paula Weir and Pedro Saavedra, Two Multi-Phase Surveys That Combine Overlapping Sample Cycles at Phase I). The...

A recent article in USA Today used the following data to illustrate the decline in the percentage of men who receive college and advanced degrees: a. Use one graph that contains two bar charts, each...

The regional sales manager for American Toys, Inc., recently collected data on weekly sales (in dollars) for the 15 stores in his region. He also collected data on the number of salesclerk work hours...