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Consider the partial differential equation with boundary conditions yu-2V²u = 12, 0

Consider the partial differential equation with boundary conditions yu-2V²u = 12, 0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter1: Fundamental Concepts Of Algebra
Section1.1: Real Numbers
Problem 30E
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| W +0 File Paste 12,1,11,1,10,1,9,1,8,1,7,1,6,1,5,1.4,1,3,1,2,1,1,1,,1,1,1,2 日 Home Insert Page Layout Cut Copy Format Painter Clipboard 05:13 PM 2022-07-23 Page: 1 of 1 Words: 12 References BIU Calibri (Body) - 14 Á Α Α΄ I U abe X₂ X³ Font Mailings Aa B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbcc AaBI AaBb CcL 1 Normal No Spaci... Heading 1 Title Subtitle Heading 2 Styles ··2·1·1·1···1·1·2·1·3·1·4·1·5·1·6·1·7·1·8·1·9·1·10 ·| · 11 · |· 12 · |· 13 · |· 14 · 1 · 15 · |-·\\ · · · 17 · · · 18. I I I A ab T Aal Document1 - Microsoft Word (Product Activation Failed) View Review I Paragraph I with boundary conditions I NUMERICAL METHODS QUESTION PLEASE HELP ANSWER BOTH QUESTION (a) and (b) BELOW: Consider the partial differential equation yu-2V²u = 12, 0<x<4, 0<y<3 x = 0 and x = 4: y = 0 and y = 3: u = 60 อน ду = 5. (a) Taking h = 1, sketch the region and the grid points. Use symmetry to minimize the number of unknowns u, that have to be calculated and indicate the u, in the sketch. (b) Use the 5-point difference formula for the Laplace operator to derive a system of equations for the U₁. | Find АА Час Replace Change Styles Select Editing ENRE G 100% - D @? +
Transcribed Image Text:| W +0 File Paste 12,1,11,1,10,1,9,1,8,1,7,1,6,1,5,1.4,1,3,1,2,1,1,1,,1,1,1,2 日 Home Insert Page Layout Cut Copy Format Painter Clipboard 05:13 PM 2022-07-23 Page: 1 of 1 Words: 12 References BIU Calibri (Body) - 14 Á Α Α΄ I U abe X₂ X³ Font Mailings Aa B-B-S ## T AaBbCcDc AaBbCcDc AaBbC AaBbcc AaBI AaBb CcL 1 Normal No Spaci... Heading 1 Title Subtitle Heading 2 Styles ··2·1·1·1···1·1·2·1·3·1·4·1·5·1·6·1·7·1·8·1·9·1·10 ·| · 11 · |· 12 · |· 13 · |· 14 · 1 · 15 · |-·\\ · · · 17 · · · 18. I I I A ab T Aal Document1 - Microsoft Word (Product Activation Failed) View Review I Paragraph I with boundary conditions I NUMERICAL METHODS QUESTION PLEASE HELP ANSWER BOTH QUESTION (a) and (b) BELOW: Consider the partial differential equation yu-2V²u = 12, 0<x<4, 0<y<3 x = 0 and x = 4: y = 0 and y = 3: u = 60 อน ду = 5. (a) Taking h = 1, sketch the region and the grid points. Use symmetry to minimize the number of unknowns u, that have to be calculated and indicate the u, in the sketch. (b) Use the 5-point difference formula for the Laplace operator to derive a system of equations for the U₁. | Find АА Час Replace Change Styles Select Editing ENRE G 100% - D @? +
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