Question: The (m 1) (m 1) tridiagonal matrix is involved in the Backward Difference method to solve the heat equation. For the stability

The (m ˆ’ 1) Ã— (m ˆ’ 1) tridiagonal matrix

is involved in the Backward Difference method to solve the heat equation. For the stability of the method we need Ï(Aˆ’1) a. Î± = 1 / 4
b. Î± = 1 / 2
c. Î± = 3/4
When is the method stable?

1+ 2a 1+2a -a A = 1+ 2a

Step by Step Solution

★★★★★

3.41 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

Using the Inverse Power method with x 0 1 0 0 1 ... View full answer

Question Has Been Solved by an Expert!

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

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

731-M-N-A-N-L-A (877).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

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

The (m 1) Ã (m 1) matrices A and B given by And are involved in the Crank-Nicolson method to solve the heat equation (see Section 12.2).Withm = 11, approximate Ï(A1 B) for each of the...

Show that the eigenvalues for the (m 1) by (m 1) tridiagonal method matrix A given by are with corresponding eigenvectors v(i), where v(i)j = sin(ijÏ/m). jsi-lorj = 1+1, 1-21, j-i, 0, oterwise...

approaching deadline please answer it ASAP Amelia, Brianna and Cathy want to use finite difference method to solve Poisson's equation + over a rectangular domain 12 {(x,y) ER?:05xs 18 and 0 Sys 9)....

Please answer all the above questions correctly providing necessary formulae, equations, expressions, diagrams, charts, graphs, tables and plots. A tubular chemical reactor (plug flow reactor with...

Please change the following code to help me obtain the graphs posted below Heat Diffusion on a Rod over the time In class we learned analytical solution of 1-D heat equation subplot (2,1,1); aa7 le...

Heat Diffusion on a Rod over the time In class we learned analytical solution of 1-D heat equation Inline image 1 In this homework we will solve the above 1-D heat equation numerically. Below is the...

Please answer each question by entering the most nearly correct answer (a, b, c, d) in the blank on the left. ____1. The approximation cos(x) 1 - x2 /2 + x4 /24 is to be used over [-1,1]. The...

Paoatnn 1 Consider the bridge truss diagrannued below: Given a vector of edema] forces [what we call the \"data\" or the \"right hand side"] b on the bridge. we can compute the forces F1. F2. . .. ....

PROBLEM 2 In this problem, we will explore a simple way to model oscillatory motion. The model in this problem could be used to approximate the motion of a sky scraper , a swinging pendulum , or a...

Suppose John tries to execute the loop below as efficiently as possible. He has 2 different machines, a MIMD machine and a SIMD machine. for (i=0; i<1000;i++) for (j=0; j<2000;j++) X_array...

Let u be a vector in an inner product space V, and let (v1, v2, ..., vn) be an orthonormal basis for V. Show that if a1 is the angle between u and vi then Cos2a1 + cos22 + . . . + cos2an = 1

An automotive insurance company wants to predict which filed stolen vehicle claims are fraudulent, based on the mean number of claims submitted per year by the policy holder and whether the policy is...

Which of the following best describes the purpose of a portfolio in project management? A. It is a temporary endeavor undertaken to create a unique product, service, or result B. It refers to the...

A Cepheid variable star is a star whose brightness alternately increases and decreases. The most easily visible such star is Delta Cepheid, for which the interval between times of maximum brightness...

In Example 4 in Section 1.3 we arrived at a model for the length of daylight (in hours) in Philadelphia on the day of the year: Use this model to compare how the number of hours of daylight is...

The motion of a spring that is subject to a frictional force or a damping force (such as a shock absorber in a car) is often modeled by the product of an exponential function and a sine or cosine...

ABC Corp. is insured under a CGL with the following limits: General Aggregate $2,000,000. Products/ Completed Operations Aggregate $2,000,000. Personal & Advertising Injury Limit $1,000,000. Each...

STATS 134-B READ COMMENTS FOR INSTRUCTIONS! PLEASE SKIP IF YOU CANT FINISH! I WILL REPORT THOSE WHO WILL FLAG THIS. THANKS NEED URGENT! 6. When attributes charts are used when _______ a) Destructive...

3.17 Insurance company losses of a particular type are to reasonable approximation normally distributed with a mean of $150 million and standard deviation of $50 million. (Assume no different between...