Explanation Given: The given boundary value problem is ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 = 0 , y > 0 , 0 < x < π and the boundary conditions are u ( 0 , y ) = f ( y ) , u x ( π , y ) = 0 and u y ( x , 0 ) = 0 . Calculation: The given boundary value problem is, ∂ 2 u ∂ x 2 + ∂ 2 u ∂ y 2 = 0 . (1) Take Fourier transform of both sides of the above equation, F { ∂ 2 u ∂ x 2 } + F { ∂ 2 u ∂ y 2 } = 0 d 2 U d x 2 − α 2 U ( x , α ) − u y ( x , 0 ) = 0 d 2 U d x 2 − α 2 U ( x , α ) = 0 Therefore, the equation is, d 2 U d x 2 − α 2 U ( x , α ) = 0 Apply Fourier cosine transform then the particular solution of the above equation is, U ( x , α ) = c 1 cosh α x + c 2 sinh α x . (2) At the given boundary condition u ( 0 , y ) = f ( y ) , U ( 0 , α ) = F ( α ) c 1 = F ( α ) Substitute the value of c 1 in equation (2), U ( x , α ) = F ( α ) cosh α x + c 2 sinh α x

9th Edition

ISBN: 9781337292405

Author: ZILL

Publisher: CENGAGE L

See similar textbooks

Videos

Question

Chapter 14.4, Problem 16E

To determine

The boundary value problem under given boundary conditions.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.4, Problem 15E

Chapter 14.4, Problem 17E

Students have asked these similar questions

18:36 G.C.A.2.ChordsSecantsandTa... จ 76 完成 2 In the accompanying diagram, AABC is inscribed in circle O, AP bisects BAC, PBD is tangent to circle O at B, and mZACB:m/CAB:m/ABC= 4:3:2 D B P F Find: mZABC, mBF, m/BEP, m/P, m/PBC ← 1 Ő

14:09 2/16 jmap.org 5G 66 In the accompanying diagram of circle O, diameters BD and AE, secants PAB and PDC, and chords BC and AD are drawn; mAD = 40; and mDC = 80. B E Find: mAB, m/BCD, m/BOE, m/P, m/PAD ← G.C.A.2.ChordsSecantsand Tangent s19.pdf (538 KB) + 4 保存... X

16:39 < 文字 15:28 |美图秀秀保存 59% 5G 46 照片完成 Bonvicino - Period Name: 6. A right regular hexagonal pyramid with the top removed (as shown in Diagram 1) in such a manner that the top base is parallel to the base of the pyramid resulting in what is shown in Diagram 2. A wedge (from the center) is then removed from this solid as shown in Diagram 3. 30 Diogram 1 Diegrom 2. Diagram 3. If the height of the solid in Diagrams 2 and 3 is the height of the original pyramid, the radius of the base of the pyramid is 10 cm and each lateral edge of the solid in Diagram 3 is 12 cm, find the exact volume of the solid in Diagram 3, measured in cubic meters. Show all work. (T 文字贴纸消除笔涂鸦笔边框马赛克去美容

Chapter 14 Solutions

DIFF.EQUAT.W/BOUNDARY-VALUE...(LL)-TEXT

Ch. 14.1 - (a) Show that erf(t)=10ted. (b) Use part (a), the...Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Use the third and fifth entries in Table 14.1.1 to...

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

The boundary value problem under given boundary conditions.

Solution Summary: The author explains the solution of the boundary value problem under given boundary conditions.

Videos

The boundary value problem under given boundary conditions.

Want to see the full answer?

Chapter 14 Solutions