Consider the following unsteadyreaction-diffusion equation:dun.Ddx²– kju³ + k2u²,.3%3DƏtThe initial and boundary conditions aregiven by: u(x, 0)u(1, t)equation with centered finite differences anduse Explicit Euler, what are the system ofequations we need to solve?1, и(0, t)= 0 > 0. If we discretize the5 and

Use the Jacobian matrix to solve the question. Assume the terms of the matrix and then solve it.

Consider the following unsteady reaction-diffusion equation: ди = D Ət – kju³ + k2u², The initial and boundary conditions are given by: u(x, 0) u(1,t) = 0 V t > 0. If we discretize the equation with centered finite differences and use Explicit Euler, what are the system of equations we need to solve? 1, и(0, t) — 5 and

Consider the following unsteady reaction-diffusion equation: ди = D Ət – kju³ + k2u², The initial and boundary conditions are given by: u(x, 0) u(1,t) = 0 V t > 0. If we discretize the equation with centered finite differences and use Explicit Euler, what are the system of equations we need to solve? 1, и(0, t) — 5 and

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Match the third order linear equations with their fundamental solution sets. 1. y" – 7y" + 12y' = 0 2. y" – y" – y' + y = 0 3. y" + y' = 0 4. y" – 7y" + y'– 7y = 0 5. ty" – y" = 0 6. y" + 3y" + 3y' +y = 0 A. e, te, t'et B. 1, cos(t), sin(t) C. e", cos(t), sin(t) D. 1, e4, e3t E. e', te', et t3 F. 1, t,
Convert the Second order ODE x''+2x'+9x+5=0 to a first order system of two equations. Use y for x'. x'(t) = ? y'(t)= ?
A. y" + 2y' + y = 0 B. y" + 2y' + 2y = 0 C. y" + 4y = 0 D. y" – 3y' + 2y = 0 Table 1: A-D are homogeneous second order linear equations.
5. Consider the system: dx - = x- y+ 3x' – 2xy² dt dy -=-x +y+3y' – 2x°y dt Show that the system has no periodic solution other than the constant ones. etion-
Use the elimination method to find a general solution for the given linear system, where differentiation is with respect to t. 2x+y'-3x-3y = e−3t x'y' +6x+3y = e3t
A. y" + 2y' + y = 0 B. y" + 2y' + 2y = 0 C. y" + 4y = 0 D. y" – 3y' + 2y = 0 Table 1: A-D are homogeneous second order linear equations.
Show that the following equations: x1(t)=e-2t+2e-t x2 (t)=e-2t+e-t They are solution of the system: x'1=-2x2 x´2=x1-3x2 And find its critical points. Please be as clear as possible and show all the steps. Thank you.
Find the general solutions to the following homogeneous constant-coefficient linear equations. (a) y() + " – y' – y = 0. (b) y(4) = 16y. (C) y4) + 23) + 3y" + 2g + y = 0. (Hint: expand (r2 +r + 1)°.)
5. Okay, time for some mathematics. We're going to focus on the interactions between the hares and their main predators, the lynx. The tool we need is differential equations (last seen when we talked about the S-I-R disease model). We will let H(t) be the density of hares at time t, and L(t) the density of lynx at time t. Our first assumption is that, if there are no lynx around, the hares grow exponentially. Hares lead to more hares and faster growth. This gives us the differential equation (trust me): HP = aH dt where a is a positive constant. Second we assume that, if there are no hares around, the lynx starve and thus their numbers decay exponentially. This gives us: TP = -bL dt
Given y₁ (t) = t² and y2(t) = t¹ satisfy the corresponding homogeneous equation of t²y" - 2y = 2-t, t > 0, the general solution to the nonhomogeneous equation can be written as y(t) = yp(t) + C₁y₁(t) + c2y2(t). Use variation of parameters to find y, (t). Yp(t) Preview =
The velocity of a particle at position r = (x, y), in two-dimensional Cartesian coordinates, is given by v = (αy,αx), where α ∈ R is a constant. What are the physical dimensions of the parameter α? Find the general form of r(t), the position of the particle, as a function of time t (hint: write v = (αy,αx) as a system of first order ODEs). What is the critical point and its nature in this system? Suppose at t = 0, r(0) = (2,0). By eliminating the variable t, find the nature of the particle’s trajectory and give a sketch of it.