7-Laplace's equation-Iterative method.... >>>QJacobi Iteration:mmmuj-1 + u-1₁j + ui+1) + uj+14Note that this formula assumes Ax = Ay.For each interior grid point (i, j), uij at the next iteration (m+1) is foundfrom (6). Once an iteration has been completed for all interior grid points,we compute the infinity norm for vector um+1- umU₁₁jm+1 =If lum+1 um < tol, where tol is a pre-defined tolerance, theiterations terminate and the solution to (5) is um+1, otherwise theiterations continue.To start the iteration (m-0) values must be given for the unknown interiorvalues of uij. These values can be set to zero or interpolated from theknown boundary values.EXAMPLE: Solve the Laplace's equation on the following small gridwith Ax = Ay using Jacobi Iteration with tol-5 x 10-³. Set startingvalues to zero for all interior points.11,3m+1 =ui.j11,2Jacobi Iteration:U14u¹= (U2,1"22,2m+18.98.4m7.26.1241.122,48.9m13U₁6.8142.1U3,48.9mmmuj-1 + U-1₁j + U+1.j + ulj +14for all interior points we have:thULT7.713.1U448.911431438.7772m= (U2,1 + U₁,2" + U3,2+U2,3)/414.1...USA8.99.29.4۱۲:۱۱9.815.1(6)(6)US,3Us,2A

In this problem, we are given a discrete distribution of heat on a grid and are asked to use the…

Answered: EXAMPLE: Solve the Laplace's equation…

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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9:17 ll LTE 4 GE0103EN Name Class. Date Enrichment 1-3 ............. Parallel Lines in Everyday Life Airplanes following a primarily cast-west route cruise at altitudes that are an odd number of thousand feet above ground level. Airplanes that are following a primarily north-south route cruise at altitudes that are an even number of thousand feet above ground level. Given each cruising altitude, state whether the airplane is traveling east-west or north-south. 3. 47,000 ft 1. 26,000 ft 2. 31,000 ft 4. 16,000 ft Assuming that all airplanes are at their cruising altitudes and are flying in straight lines, answer Exercises 5-9 always, sometimes, or never. 5. The paths of two airplanes flying directly east-west are 2 coplanar. 6. The paths of two airplanes flying directly north-south are ?_ skew. 7. The paths of an airplane flying directly north-south and an airplane flying directly east-west are ? coplanar. 8. The paths of an airplane flying directly north-south and an airplane flying…
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3. Define a variable y from 0 to 20 with steps of 0.2. Also, define the time variable t from 0 to 10 with steps of 0.1. Plot the graph of y v/s t. a. Label the x-axis and y-axis.
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Question 14. Let 1 3√2 1 -@)-0- 3√2 4 3√2 = 1 3 U3 = 2 0 (b) Let x = (1, 1, 1)T. Write x as a linear combination of u₁, u2, and u3 using Theorem 21.13 and use Parseval's formula to compute ||x||.
Given that the characteristic equation have the following complemantary solution, what are its roots? y = (c1 + C2x + c3x?)e + (c4 + c5x)e2 + C6e O a. 1,-1,-1,-1,-2,-2 O b. 1,1,-1,2,2,-2 O c. 1,1,1,-1,2,2 O d. -1,-1,-1,2,2,-2
You should work through the "Lesson 10 - Further Linear Algebra" self-paced learning module on UNSW Moodle and revise Week 4 Online Tutorial before attempting this question. You may need the commands Gaussi anElimination and LinearSolve in the Line ar Al gebra package. Suppose that S = {P1, P2, P3, P4}, where +116 a3 - 254 x4 P2 (x) = -39 + 95 x + 75 a² – 43 x3 + 34 x4, P1(x) = -196+ 299 x + 57 x2 P3(x) = -194+ 258 x – 94 x2 – 289 x³ – 129 a4 P4 (x) = 259 + 207 x + 285 x² – 113 x3 + 213 z4 and p(x) = 21949 – 45591 x – 9401 x² + 16428 x³ + 16206 x4 To avoid typing errors, you can copy and past the following sequences to your Maple worksheet. -196, 299, 57, 116, -254 -39, 95, 75, -43, 34 -194, 258, -94, -289, -129 259, 207, 285, -113, 213 21949, -45591, -9401, 16428, 16206 The polynomial p is a linear combination of S written in the form ap1 + Bp2 + YP3 + Sp4 Find a possible set of values for a, B, y, 8. Enter the values of a, B, y, 8 as a sequence in the box below [a, B, Y, 8] =
Question 2 Tiffany organizes a street collection for a mental health charity. The collection takes place in Kingston on a particular Saturday. Volunteers, with collecting tins, stand in busy places and ask passers-by for donations. The following table shows, for eight volunteers, the times, x minutes, they spent collecting together with amounts to the nearest hundred-dollar, y, they collected. A. B. C. 65 21 187 52 55 8 143 28 X y Determine the product-moment coefficient 90 10 74 19 88 17 90 47 Determine the linear regression equation that relates to the data. If a volunteer spent 100 minutes, estimate how much money would be collected?
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