1. Consider the following advection equation: u+au = 0 _u(x,0) = {-4(x+8) (x + 9), if-9x-8...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
1. Consider the following advection equation: u+au = 0 _u(x,0) = {-4(x+8) (x + 9), if-9x-8 otherwise. Use any of the finite difference methods: Upwind, Lax-Friedrich, Lax-Wendroff, Leapfrog to solve the problem for -10 x-10 using a grid where r = = 0.95, a = 1. Plot your solution at time t = 10. 2. Consider the following equation du t subject to the conditions = Pu x z (0,1), t> 0, u(x, 0) u(0. t) = 0 = u(1, t), t20 u(x,0) = x(1-x), 0x1. Discretize the given problem both with either explicit or implicit finite difference schemes. Implement these schemes through MATLAB to find the numerical solution of the given problem. Plot your solutions at t = 0.4 and compare them with the exact solution given by u(x, t) = x(1-x)e-t. 3. Consider the Klein-Gordon equation Pu Fu x t along with the boundary and initial conditions given as u(0,t) = u(1, t) = 0, t 0. +4u, 0 0, Cos - {1 (1-COM (-)). XOSES. if a 2 a 0, otherwise. u(x,0) = 0, 0x 1. Determine and plot the numerical solution up to t= 1.7. Take a = 0.09. 1. Consider the following advection equation: u+au = 0 _u(x,0) = {-4(x+8) (x + 9), if-9x-8 otherwise. Use any of the finite difference methods: Upwind, Lax-Friedrich, Lax-Wendroff, Leapfrog to solve the problem for -10 x-10 using a grid where r = = 0.95, a = 1. Plot your solution at time t = 10. 2. Consider the following equation du t subject to the conditions = Pu x z (0,1), t> 0, u(x, 0) u(0. t) = 0 = u(1, t), t20 u(x,0) = x(1-x), 0x1. Discretize the given problem both with either explicit or implicit finite difference schemes. Implement these schemes through MATLAB to find the numerical solution of the given problem. Plot your solutions at t = 0.4 and compare them with the exact solution given by u(x, t) = x(1-x)e-t. 3. Consider the Klein-Gordon equation Pu Fu x t along with the boundary and initial conditions given as u(0,t) = u(1, t) = 0, t 0. +4u, 0 0, Cos - {1 (1-COM (-)). XOSES. if a 2 a 0, otherwise. u(x,0) = 0, 0x 1. Determine and plot the numerical solution up to t= 1.7. Take a = 0.09.
Expert Answer:
Answer rating: 100% (QA)
To solve these partial differential equations PDEs using finite d... View the full answer
Related Book For
Posted Date:
Students also viewed these mathematics questions
-
When mixing two types of atoms, say A and B, will atoms always diffuse from regions of higher concentrations to regions of lower concentrations? Explain either in words or with a graph.
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
Consider a world with two time periods and two possible states at each time t = 0, 1, 2. There are only two assets to invest. One is risk free borrowing and lending at the risk-free rate ri, i = 0,...
-
Route Canal Shipping Company has the following schedule for aging of accounts receivable: AGE OF RECEIVABLES APRIL 30, 2001 a. Fill in column (4) for each month. b. If the firm had $1,440,000 in...
-
A car traveling 88 km/h is 110 m behind a truck traveling 75 km/h. how long will it take the car to reach the truck?
-
A uniform rod of mass m is supported by a pin at A and a spring of constant k at B and is connected at D to a dashpot of damping coefficient c. Determine in terms of m, k, and c, for small...
-
On December 31, Casper, Inc., issued \(\$ 300,000\) of eight percent, ten-year bonds for \(\$ 262,613\), yielding an effective interest rate of ten percent. Semiannual interest is payable on June 30...
-
Single Audit, Internet Case. A not-for-profit organization has hired you to conduct an audit. The audit has been requested by the organizations board of directors. A mission of the organization is to...
-
Ch 10 Homework eBook Learning Objective 3 1. CEX.10.01.ALGO 2. CEX.10.02.ALGO 3. CEX.10.03.ALGO 4. CEX.10.04.ALGO 5. CEX.10.05.ALGO 3. CEX.10.06.ALGO of Capital and Economic Value Added (EVA)...
-
Tinkle-Tinkle Glass Company makes glass globe paper weights for desks. The company uses a job-order cost system and predetermined overhead rates apply manufacturing overhead cost to jobs. The...
-
Explain briefly when a company recognizes its associates for their hard work, does it add value to the organization?
-
Tendering is the main method of procurement in the Kenyan public sector. You are required to; State the requirements that a supplier should fulfill in order to qualify for tendering in Kenya, What is...
-
What is not a hedging technique for accounts payable? What is the agreement established in 1972 to maintain the value of the currency in parameters established between the subscribed countries?
-
Discuss the role of finance in business, so I can answer it for class? Also, what is the purpose of financial management? I have to also describe the kinds of activities that financial management...
-
When an ETF manager decides to launch a new fund, it requires a partnership with a "designated dealer". What is the role of a "designated dealer"?
-
A perfectly competitive firm uses coal to generate electricity. Its supply curve is Q = 100P - 1350, where Q is the quantity produced (units of electricity per year), and P is the market price of...
-
The population of Detroit, Michigan, decreased from 1,027,974 in 1990 to 688,701 in 2013 (Source: U.S. Census Bureau). Find the average rate of change in the population of Detroit, Michigan, over the...
-
Consider the linear system Ax = e1 based on the 10 Ã 10 pentadiagonal matrix (a) For what values of z are the Jacobi and Gauss- Seidel methods guaranteed to converge? (b) Set z = 4. How many...
-
Find the plane z = a + fix + yy that best approximates the following functions on the square S = {-1 ¤ x ¤ 1, -1 ¤ y ¤ 1 using the L2 norm to measure the least squares...
-
For the following data values, construct the interpolating polynomial in Lagrange form: (a) (b) (c) (d) (e) t-3 2 5 yi y5 25 y2 -1 5 ,-2 -1 02 y,1-1-2213
-
How does monopoly lead to inefficiencies?
-
What is the welfare loss in monopoly?
-
Does monopoly retard innovation?
Study smarter with the SolutionInn App