Whether the Backward Difference Method unconditionally stable for the heat equation if c < 0 .

Question

Want to see the full answer?

Answer 1

Question

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

31.

On Feb. 8, this year, at 6am in the morning all UiB meteorology professors met to discuss a highly unfortunate and top-urgent crisis: Their most precious instrument, responsible for measuring the air temperature hour-by- hour, had failed - what if the Bergen public would find out? How would they plan their weekend without up-to-date air temperature readings? Silent devastation - and maybe a hint of panic, also - hung in the room. Apprentice Taylor, who - as always - was late to the meeting, sensed that this was his chance to shine! Could they fake the data? At least for some hours (until the measurements would work again)? He used to spend a lot of time online and thus knew the value of fake data, especially when it spread fast! He reminded the crying professors of a prehistoric project with the title "Love your derivatives as you love yourself!" - back then, they had installed top-modern technology that not only measured the air temperature itself, but also its 1st, 2nd, 3rd, 4th, and…

Consider a forest where the population of a particular plant species grows exponentially. In a real-world scenario, we often deal with systems where the analytical function describing the phenomenon is not available. In such cases, numerical methods come in handy. For the sake of this task, however, you are provided with an analytical function so that you can compare the results of the numerical methods to some ground truth. The population P(t) of the plants at time t (in years) is given by the equation: P(t) = 200 0.03 t You are tasked with estimating the rate of change of the plant population at t = 5 years using numerical differentiation methods. First, compute the value of P'(t) at t = 5 analytically. Then, estimate P'(t) at t = 5 years using the following numerical differentiation methods: ⚫ forward difference method (2nd-order accurate) 3 ⚫ backward difference method (2nd-order accurate) ⚫ central difference method (2nd-order accurate) Use h = 0.5 as the step size and round all…

Answer 2

Question

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Answer 6

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Answer 7

Chapter 8.1, Problem 4E

To determine

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Answer 8

Expert Solution & Answer

Answer 9

Expert Solution & Answer

Answer 10

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 11

Ch. 8.1 - Prove that the functions (a) u(x,t)=e2t+x+e2tx,...Ch. 8.1 - Prove that the functions (a) u(x,t)=etsinx, (b)...Ch. 8.1 - Prove that if f(x) is a degree 3 polynomial, then...Ch. 8.1 - Prob. 4E Ch. 8.1 - Verify the eigenvector equation (8.13).Ch. 8.1 - Show that the nonzero vectors vj in (8.12 ), for...Ch. 8.1 - Prob. 1CP Ch. 8.1 - Consider the equation ut=uxx for 0x1, 0t1 with the...Ch. 8.1 - Prob. 3CP Ch. 8.1 - Use the Backward Difference Method to solve the...

Whether the Backward Difference Method unconditionally stable for the heat equation if c < 0 .

Solution Summary: The author explains that the Backward Difference Method is not unconditionally stable for the heat equation when c0.

Concept explainers

Videos

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Want to see the full answer?

Chapter 8 Solutions

Whether the Backward Difference Method unconditionally stable for the heat equation if c &lt; 0 .

Solution Summary: The author explains that the Backward Difference Method is not unconditionally stable for the heat equation when c0.

Concept explainers

Videos

To explain: Whether the Backward Difference Method unconditionally stable for the heat equation if c <0 .

Want to see the full answer?

Chapter 8 Solutions

Whether the Backward Difference Method unconditionally stable for the heat equation if c < 0 .