Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 8.1, Problem 6CP
a.
To determine
To calculate: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at
b.
To determine
To find: The solution of the given problem using Crank-Nicolson method and also create a table of the exact value, the approximate value and the error at
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionChapter 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
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.Similar questions
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:CengageMathematics For Machine TechnologyAdvanced MathISBN:9781337798310Author:Peterson, John.Publisher:Cengage Learning,
- Glencoe Algebra 1, Student Edition, 9780079039897...AlgebraISBN:9780079039897Author:CarterPublisher:McGraw HillAlgebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningAlgebra and Trigonometry (MindTap Course List)AlgebraISBN:9781305071742Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
Mathematics For Machine Technology
Advanced Math
ISBN:9781337798310
Author:Peterson, John.
Publisher:Cengage Learning,
Glencoe Algebra 1, Student Edition, 9780079039897...
Algebra
ISBN:9780079039897
Author:Carter
Publisher:McGraw Hill
Algebra for College Students
Algebra
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Cengage Learning
Algebra and Trigonometry (MindTap Course List)
Algebra
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:Cengage Learning
01 - What Is A Differential Equation in Calculus? Learn to Solve Ordinary Differential Equations.; Author: Math and Science;https://www.youtube.com/watch?v=K80YEHQpx9g;License: Standard YouTube License, CC-BY
Higher Order Differential Equation with constant coefficient (GATE) (Part 1) l GATE 2018; Author: GATE Lectures by Dishank;https://www.youtube.com/watch?v=ODxP7BbqAjA;License: Standard YouTube License, CC-BY
Solution of Differential Equations and Initial Value Problems; Author: Jefril Amboy;https://www.youtube.com/watch?v=Q68sk7XS-dc;License: Standard YouTube License, CC-BY