z(k, l) = 4*µk+l. %3D essions of this form allows the conclusion z(k, l) = 4* f(k + l),

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
icon
Concept explainers
Question

Show me the steps of determine green 

5.3.2 Еxample B
The equation
z(k + 1, l) = 4z(k, l + 1)
(5.84)
leads to the conclusion that A=
4µ. Therefore, equation (5.84) has the special
solutions
2(k, l) = 4*µk+e.
(5.85)
Summing expressions of this form allows the conclusion
E
z(k, l) = 4* f(k + l),
(5.86)
where f is an arbitrary function of k + l.
The separation-of-variables method, where zp(k, l) = CkDe, gives
Ck+1De = 4Ck De+1»
(5.87)
which can be written in either of the forms
4De+1
De+1
De
Ck+1
Ck
Ck+1
= a.
(5.88)
or
4Ck
De
The respective solutions to these equations give
z(k, l) = 4*ak+e
or z(k, l) = 4lak+e.
(5.89)
Summing over a allows us to obtain the general solution
z(k, l) = 4* f (k + e)
or z(k, l) = 4- g(k, l),
(5.90)
where f and g are arbitrary functions of k + l.
Transcribed Image Text:5.3.2 Еxample B The equation z(k + 1, l) = 4z(k, l + 1) (5.84) leads to the conclusion that A= 4µ. Therefore, equation (5.84) has the special solutions 2(k, l) = 4*µk+e. (5.85) Summing expressions of this form allows the conclusion E z(k, l) = 4* f(k + l), (5.86) where f is an arbitrary function of k + l. The separation-of-variables method, where zp(k, l) = CkDe, gives Ck+1De = 4Ck De+1» (5.87) which can be written in either of the forms 4De+1 De+1 De Ck+1 Ck Ck+1 = a. (5.88) or 4Ck De The respective solutions to these equations give z(k, l) = 4*ak+e or z(k, l) = 4lak+e. (5.89) Summing over a allows us to obtain the general solution z(k, l) = 4* f (k + e) or z(k, l) = 4- g(k, l), (5.90) where f and g are arbitrary functions of k + l.
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Points, Lines and Planes
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,