3rd Edition

ISBN: 9780134696454

Author: Sauer, Tim

Publisher: Pearson,

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Textbook Question

Chapter 8.4, Problem 5CP

Solve the Brusselator equations for D p = 1 , D q = 8 , C = 4.5

and (a) K = 4 (b) K = 5 (c) K = 6 (d) K = 6.5 . Using homogeneous Neumann boundary conditions and initial conditions p ( x , y , 0 ) = 1 + cos π x cos π y , q ( x , y , 0 ) = 2 + cos 2 π x cos 2 π y , estimate the least value T for which | p ( x , y , t ) − C | < 0.01 for all t > T .

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Chapter 8.4, Problem 4CP

Chapter 8.4, Problem 6CP

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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. 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...

Ch. 8.1 - Use the Crank-Nicolson Method to solve the...Ch. 8.1 - Prob. 6CP Ch. 8.1 - Prob. 7CP Ch. 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. 3CP Ch. 8.2 - Prob. 4CP Ch. 8.3 - Show that u(x,y)=ln(x2+y2) is a solution to the...Ch. 8.3 - Prob. 2E Ch. 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. 7E Ch. 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. 11E Ch. 8.3 - Prob. 12E Ch. 8.3 - Prob. 13E Ch. 8.3 - Solve the Laplace equation problems in Exercise 3...Ch. 8.3 - Prob. 2CP Ch. 8.3 - Prob. 3CP Ch. 8.3 - Prob. 4CP Ch. 8.3 - Prob. 5CP Ch. 8.3 - The steady-state temperature u on a heated copper...Ch. 8.3 - Prob. 7CP Ch. 8.3 - Prob. 8CP Ch. 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. 12CP Ch. 8.3 - Prob. 13CP Ch. 8.3 - Solve the elliptic partial differential equations...Ch. 8.3 - Prob. 15CP Ch. 8.3 - Prob. 16CP Ch. 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. 3E Ch. 8.4 - Prob. 4E Ch. 8.4 - Prob. 5E Ch. 8.4 - Prob. 6E Ch. 8.4 - Prob. 1CP Ch. 8.4 - Prob. 2CP Ch. 8.4 - Solve Fishers equation (8.69) with...Ch. 8.4 - Prob. 4CP Ch. 8.4 - Solve the Brusselator equations for...Ch. 8.4 - Prob. 6CP

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Solution Summary: The author explains the Matlab programme used for the calculation of Newton iteration Brusselator using backward difference method.

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Chapter 8 Solutions