Register

Homework Help Question and Answers

Submit a new Query

Recent Homework Help Question & Answers


Question 35740

posted 1 years ago

e. For each of the four time-steps considered, plot (on the same axes) the difference be-tween the exact solution and the numerical solution.

View answer

Question 35737

posted 1 years ago

. The differential equation describing heat conduction,
\frac{\partial u}{\partial t}=c^{2} \frac{\partial^{2} u}{\partial x^{2}}, \quad 0 \leq x \leq 1, \quad t \geq 0
subject to the conditions
\frac{\partial u}{\partial x}(0, t)=0, \quad u(1, t)=9 \cos (1) e^{-c^{2} t}, \quad t \geq 0
and
u(x, t)=9 e^{-c^{2} t} \cos x
has the (exact) solution
u(x, 0)=9 \cos x, \quad 0 \leq x \leq 1

View answer

Question 35738

posted 1 years ago

c. Write a suitably commented Matlab program to implement this scheme. Print out a copy of your code to include with your homework submission.

View answer

Question 35736

posted 1 years ago

a. For this homework, you will need a random number, c, which can be generated usingthe last four digits of your student registration number. If, for example, your registrationnumber is 012345678, type the following commands in a MATLAB command window.
\gg \text { rand ('seed', } 5678 \text { ); }
\gg c=1+5^{*} r a n d
This will generate the following output.

View answer

Question 35739

posted 1 years ago

d. Run the Matlab code to perform FOUR iterations of the Crank-Nicolson scheme for this problem. For each time-step considered, print out a table showing the exact solution, the numerical solution, and the difference between these values for each mesh point. These should show at least 4 iterations of the numerical method.

View answer

Question 38315

posted 1 years ago

For a long, thin insulated rod, a parabolic equation can be employed to characterize time -variable problems for a heat conduction equation in one dimensional which requires approximation for the second derivative in space and the first derivative in time.
а.In the calculation of heat conduction equation, describe the assumption that need to be considered.
b.For one dimensional heat equation in insulated thin rod, derive equations for the first, internal and the last point of the grid.
d.Select thebest method from the TWO (2) numerical methods in Part (2)(c). Justify your answer.

View answer

Question 38314

posted 1 years ago

In the process of making a mixture, the concentration of sodium x g/L is given as a function of time by
\frac{d x}{d t}=28-2.5 x
Given the initial time, t = 0 minute, the concentration of sodium in the tank is 45| L. Choose a step size in a range of 1 <h< 3 minutes for the interval from 0 to 3h minutes,
а.Calculate the sodium concentration using the TWO (2) numerical methods known as Runge Kutta 4th order method and Euler's method.
b.Describe ONE (1) advantage and ONE (1) disadvantage for the TWO(2) numerical methods in Part (1)(a) respectively.
c.Determine the best method from the TWO (2) numerical methods in Part (1)(b) based on true percent relative error. Justify your answer.

View answer

Question 33307

posted 1 years ago

In this example of the free-falling parachutist, we assumed that the acceleration due to gravity was a constant value. Although this is a decent approximation when we are examining falling objects near the surface of the earth, the gravitational force decreases as we move above sea level. A more general representation based on Newton's inverse square law of gravitational attraction can be written as presented in Eq.1
g(x)=g(0) \frac{R^{2}}{(R+x)^{2}}
\frac{d v}{d t}=g-\frac{c}{m} v
where g(x) = gravitational acceleration altitude x (in m) measured upward from the earth's surface (m/s²), g(0)=gravitational acceleration at the earth's surface (9.81 m/s³),and R = the earth’s radius (6.37 x 106 m).
(a)In a fashion similar to the derivation of (Eq. 2) use a force balance to derive a differential equation for velocity as a function of time that utilizes this more complete representation of gravitation. However, for this derivation, assume that upward velocity is positive. (20 points)
(b)For the case where drag is negligible, use the chain rule to express the differential equation as a function of altitude rather than time. Recall that the chain rule is:
\frac{d v}{d t}=\frac{d v}{d x} \frac{d x}{d t} \text { (25 points) }
(c)Use calculus to obtain the closed form solution where v = vo at x = 0.
(d)Use Euler's method to obtain a numerical solution from x = 0 to 100.000 m.using a step of 10,000 m where the initial velocity is 1500 m/s upward. (25
(e)Compare your result with the analytical solution.

View answer

Question 30154

posted 1 years ago

s.) (Problem 5.13) The velocity v of a falling parachutist is given by
v=\frac{g m}{c}\left(1-e^{-\left(\frac{c}{m}\right) t}\right)
where g = 9.8 m/s². For a parachutist with a drag coefficient c = 15 kg/s, compute the mass m so that the velocity is v = 35 m/s at t=9 s. Write MATLAB programs using both the bisection method and the false-position method to determine m to a level of relative error ɛ, <= 0.1%. Compare the two methods and discuss.

View answer

Question 30153

posted 1 years ago

\text { Determine the real roots of } f(x)=-0.6 x^{2}+2.4 x+5.5
a) Graphically.
b) Using the quadratic formula;
c) Write a MATLAB function using the bisection method to determine the highest root. The function should take two inputs of x1, Xu, the max number of iterations, and output the root, estimated error, and true error.
d) Employ initial guesses of xỊ = 5 and xu = 10, call the function you write in part (c) to compute the estimated error and true error at 1s', 5th, 10th, and 30th iteration respectively.

View answer

Questions not Found

Most popular subject

Thermodynamics

Essay/Summary

Mechanics

Complex Analysis

Engineering Economics

Calculus

Modern Physics

General Chemistry

Strength Of Materials

Fluid Mechanics

x