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.141,3241,221.48.98.47.26.1141.112,48.9W₂26.812.113,48.9U7.7U3.1U4A8.9WAS8.7144.1USA8.99.29.49.8U5.115,3us2

As per the question we have to find the solution to the discretized Laplace's equation at 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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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] =
Apply Lagrange's equations, to show that the equations of motion of the double pendulum of Fig. 28-10 are given by 01 m1 P1 %3D (m1 + m2)l81 + malz82 + (m1 + m2) g®1 = 0 l81+ lg82 + g®2 = 0 m2 P2 and %3D for small angles 01, 02.
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EXAMPLE: Solve the Laplace's equation on the following small grid with Ax = Ay using Jacobi Iteration with tol=5 x 10-3. Set starting values to zero for all interior points. 141,3 241,2 21.4 8.9 8.4 7.2 6.1 1₁.1 142,4 8.9 6.8 12.1 13,4 8.9 u 7.7 U3.1 U4A 8.9 8.7 USA 8.9 9.2 9.4 9.8 15.1 U5,3 us2