The application of a finite-difference scheme to the heat equation on a three-pointgrid results in the following system of equations:u₁+¹=[A]uwhereTAJ-|and r= a^t/(Ax)². Determine the stability of this scheme.1ľ01-2r T0 1

The given system is:where To find: The stability of the the system.Concept:To determine the…

Answered: The application of a finite-difference…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Let r,, r, and r, be the roots of x' +3x² -5x-4=0, construct the equation whose roots are: 7 (r, + r3 ), rz (r, +x) and r, (r +r, ). F12 PrtScr Insert Delete F8 F9 F10 F11
Su Q: Evalute du (x-2)-
1. Is L = {1 − 2x + 3x^2, x − 2x^2, 2 − 5x + 8x^2} linearly independent? If yes, show why. If not, show a dependence relationship. Is L = {1 + 2x + 2x^2, x − 2x^2, −2 − 3x − 5x^2} linearly independent? If yes, show why. If not, show a dependence relationship.
check whether or not the given equations are homogeneous of some degree, and if yes, use an appropriate variable change to solve them
solve it so fast pls
What is the coefficient of x4y2z6 in the expansion of (3x2 + 2y + 3z3)6 ?
Find the 2nd solution using reduction of order. +y' = 0; y1 = Inx For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BI U Paragraph I * O 6 Q Arial 14px o WORDS POWERED BY TINY
Airodyne Wind, Inc., has wind tunnels that can operate vertically or horizontally for evaluating the effects of air flow on a component's PCB response and reliability. The company expects to build a new tunnel that will be outfitted with multiple sensor ports. For the estimates below, calculate the equivalent annual cost of the project. First Cost Replacement Cost, Year 2 AOC per Year Salvage Value Life, Years Interest Rate The equivalent annual cost of the project is $ $-250,000 $-330,000 $-940,000 $280,000 5 11%
LYn+1 . You are monitoring the movement of a 2D alien. After months of analysis, you have come up with a the following equation- Xn+1 7 2] Yn Which means, if at nth minute, the 2D aliean is at point (1, 2), at n+ 1thminute, they will be at point (7 x 1+2× 2, –4 × 1+1× 2)cint (11, –2) If you diagonalize the matrix that's been mentioned above, it should look like this - a e 1 0 d -1 f] Let's say, at minute 0, the 2D alien is at point (1,1). Let point (X5, Y5) be its position at minute 5. 1(a) What is the value of X_5 and Y_5 ?
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
Find a general solution of the system: x' =1²2 =21* L2
= 12. (a) Find the unique quadratic polynomial y ax²+bx+c that passes through the three points (1, 1), (3,5), and (-2, 0) in the x-y plane. (Hint: this will involve a linear system where a, b, and c are the unknowns.) (b) How many data points (x, y) should be needed to uniquely determine the coefficients of an nth degree polynomial anx" +an-1² -1xn-1+...+ a₁x+ao? Explain your answer in terms of linear systems.

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The application of a finite-difference scheme to the heat equation on a three-point grid results in the following system of equations: u+¹=[A]u where 0 i] T and r= a^t/(Ax)². Determine the stability of this scheme. [A]= 10 1-2r 0 0 1