Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
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Chapter 8.1, Problem 8CP
Setting
in the population model (8.26), use Crank-Nicolson to find the minimum patch size that allows the population to survive. Compare with the rule (8.27).
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Chapter 8 Solutions
Numerical Analysis
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. 4ECh. 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. 1CPCh. 8.1 - Consider the equation ut=uxx for 0x1, 0t1 with the...Ch. 8.1 - Prob. 3CPCh. 8.1 - Use the Backward Difference Method to solve the...
Ch. 8.1 - Use the Crank-Nicolson Method to solve the...Ch. 8.1 - Prob. 6CPCh. 8.1 - Prob. 7CPCh. 8.1 - Setting C=D=1 in the population model (8.26), use...Ch. 8.2 - Prove that the functions (a) u(x,t)=sinxcos4t, (b)...Ch. 8.2 - Prove that the functions (a) u(x,t)=sinxsin2t, (b)...Ch. 8.2 - Prove that u1(x,t)=sinxcosct and u2(x,t)=ex+ct are...Ch. 8.2 - Prove that if s(X) is twice differentiable, then...Ch. 8.2 - Prove that the eigenvalues of A in (8.33) lie...Ch. 8.2 - Let be a complex number. (a) Prove that if +1/ is...Ch. 8.2 - Solve the initial-boundary value problems in...Ch. 8.2 - Solve the initial-boundary value problems in...Ch. 8.2 - Prob. 3CPCh. 8.2 - Prob. 4CPCh. 8.3 - Show that u(x,y)=ln(x2+y2) is a solution to the...Ch. 8.3 - Prob. 2ECh. 8.3 - Prove that the functions (a) u(x,y)=eysinx, (b)...Ch. 8.3 - Prove that the functions (a) u(x,y)=exy, (b)...Ch. 8.3 - Prove that the functions (a) u(x,y)=sin2xy, (b)...Ch. 8.3 - Prove that the functions (a) u(x,y)=ex+2y, (b)...Ch. 8.3 - Prob. 7ECh. 8.3 - Show that the barycenter of a triangle with...Ch. 8.3 - Prove Lemma 8.9 .Ch. 8.3 - Prove Lemma 8.10.Ch. 8.3 - Prob. 11ECh. 8.3 - Prob. 12ECh. 8.3 - Prob. 13ECh. 8.3 - Solve the Laplace equation problems in Exercise 3...Ch. 8.3 - Prob. 2CPCh. 8.3 - Prob. 3CPCh. 8.3 - Prob. 4CPCh. 8.3 - Prob. 5CPCh. 8.3 - The steady-state temperature u on a heated copper...Ch. 8.3 - Prob. 7CPCh. 8.3 - Prob. 8CPCh. 8.3 - Solve the Laplace equation problems in Exercise 3...Ch. 8.3 - Solve the Poisson equation problems in Exercise 4...Ch. 8.3 - Solve the elliptic partial differential equations...Ch. 8.3 - Prob. 12CPCh. 8.3 - Prob. 13CPCh. 8.3 - Solve the elliptic partial differential equations...Ch. 8.3 - Prob. 15CPCh. 8.3 - Prob. 16CPCh. 8.3 - For the elliptic equations in Exercise 7, make a...Ch. 8.3 - Solve the Laplace equation with Dirichlet boundary...Ch. 8.4 - Show that for any constant c, the function...Ch. 8.4 - Show that over an interval [ x1,xr ] not...Ch. 8.4 - Prob. 3ECh. 8.4 - Prob. 4ECh. 8.4 - Prob. 5ECh. 8.4 - Prob. 6ECh. 8.4 - Prob. 1CPCh. 8.4 - Prob. 2CPCh. 8.4 - Solve Fishers equation (8.69) with...Ch. 8.4 - Prob. 4CPCh. 8.4 - Solve the Brusselator equations for...Ch. 8.4 - Prob. 6CP
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- Show all workarrow_forwardQ4: Discuss the stability critical point of the ODES x + sin(x) = 0 and draw phase portrait.arrow_forwardUsing Karnaugh maps and Gray coding, reduce the following circuit represented as a table and write the final circuit in simplest form (first in terms of number of gates then in terms of fan-in of those gates). HINT: Pay closeattention to both the 1’s and the 0’s of the function.arrow_forward
- Recall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forwardTheorem 1: A number n ∈ N is divisible by 3 if and only if when n is writtenin base 10 the sum of its digits is divisible by 3. As an example, 132 is divisible by 3 and 1 + 3 + 2 is divisible by 3.1. Prove Theorem 1 2. Using Theorem 1 construct an NFA over the alphabet Σ = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}which recognizes the language {w ∈ Σ^(∗)| w = 3k, k ∈ N}.arrow_forwardRecall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n (=15) is the product of the two prime numbers 3 and 5.1. Find an encryption key e for for the pair (e, n)2. Find a decryption key d for for the pair (d, n)3. Given the plaintext message x = 3, find the ciphertext y = x^(e) (where x^e is the message x encoded with encryption key e)4. Given the ciphertext message y (which you found in previous part), Show that the original message x = 3 can be recovered using (d, n)arrow_forward
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