Numerical Analysis
3rd Edition
ISBN: 9780134696454
Author: Sauer, Tim
Publisher: Pearson,
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
Chapter 8.2, Problem 3CP
To determine
To find: the solution by taking IVP values by FEM method using in matlab program.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Find the approximation for the Green's function of the
one-dimensional acoustic wave equation in the case where
velocity is given by: c(x) = aebx , where a and b are real
numbers and a > 0. Analyze each case, b 0, in detail.
Sketch the curve with the vector equation r(t) = cos(t)i − cos(t)j + sin(t)k. Show the direction of increasing t with an arrow drawn on your curve.
The graph of f (θ) = Acos θ + B sin θ is a sinusoidal wave for any constants A and B. Confirm this for (A,B) = (1, 1), (1, 2), and (3, 4) by plotting f .
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
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
- = 2. (Section 14.4) Let curve C be described by vector function(t) (cost 1, sint, ³/2) on 0 ≤ t ≤ b. Find the value(s) of b so that the length of the curve on the given interval is 18 units.arrow_forwardRepresent the plane curve by a vector-valued function. x2 /16−y2/ 4= 1arrow_forward3, Let u(t) = 2t°i+ (t- 1)j- 8k. Compute the derivative of the following function. (118 + 7t) u(t) Select the correct choice below and fill in the answer box(es) to complete your choice. The derivative is the vector-valued function ( Di+ ( Di+ ( k. O B. The derivative is the scalar functionarrow_forward
- A projectile of mass m is launched from an initial position r0 with an initial velocity v0. Find its position vector as a function of time.arrow_forwardFind an equation for the tangent plane at the point P and scalar parametric equations for the normal line. := (,? + y² )² ; P = (1,1,4) .arrow_forward5. A stone is thrown vertically downwards with a velocity of 10 m./sec. , and gravity produces on it an acceleration of 9.8 m./sec.: a) what is the velocity after 1, 2,3, t sec. ? b) sketch the velocity -time graph. (ans.: 19.8, 29.6, 39.4,10+9.8t)arrow_forward
- A particle started at A(1,0) circled the origin once an d returned toA(1,0) .what were the change in its coordinatesarrow_forwardA particle moves in the xy− plane according to the law x=at, y=bt2, where a>0, b>0. Determine the particle’s trajectory y(x) and sketch its graph. Determine the speed of the particle as a function of time. Find the angle ϕ between the velocity vector and the x−axis.arrow_forwardDuring the time period from t = 0 to t = 5 seconds, a particle moves along the path given by x(t)=2cos(ét) and y(t)=4sin(ät). Find the velocity vector for the particle at any time t.arrow_forward
- Find the directional derivative of g(a, b) = cos(3a + 4b) at the π point ( along the direction of the vector (-4,-3)arrow_forwardFind the maximum rate of change of f at the given point and the direction in which it occurs. f(s, t) = S s² + t²' 2 maximum rate of change direction vector (-5,5)arrow_forwardSketch the vector-valued function r(t) = ⟨cos(t), 1, sin(t)⟩, indicating the orientation of the curve with an arrow.arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Algebra & Trigonometry with Analytic GeometryAlgebraISBN:9781133382119Author:SwokowskiPublisher:Cengage
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:9781133382119
Author:Swokowski
Publisher:Cengage
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