Explain to me how it became like this ??? 1LnPr,s(Pr+1,s + Pr-1,s + Pr,s+1 + Pr,s-1 – 4P,,s)|(Ax)?2(xr+1 - }) + (v. - )?+ (ys – )+ (x,-1 -)°+ (y. –)*+ (x, – )° + (y.+1 - )+ (x, – ) + (y-1- )-4 (r, – })° + (v. – })*)221(Ax)?2(x, + Ax – })²+ (ys – })*22+ (x, – Ar -) + (y. – })1) 2– })?12+ (x, – )´ + (ys + Ax+ (x, – }) + (y. - Ar – })²(Ar)²12|(4, - })° + (y. – })*)-44,||

Name: Explain to me how it became like this ??? 1LnPr,s(Pr+1,s + Pr-1,s + Pr
Uploaded: 2024-03-20T07:07:37.000Z
Channel: Bartleby
Description: Explain to me how it became like this ??? 1LnPr,s(Pr+1,s + Pr-1,s + Pr,s+1 + Pr,s-1 – 4P,,s)|(Ax)?2(xr+1 - }) + (v. - )?+ (ys – )+ (x,-1 -)°+ (y. –)*+ (x, – )° + (y.+1 - )+ (x, – ) + (y-1- )-4 (r, – })° + (v. – })*)221(Ax)?2(x, + Ax – })²+ (ys – })*2

Given that, Lhϕr, s=1△x2ϕr+1,s+ϕr-1, s+ϕr, s+1+ϕr, s-1-4ϕr,…

Answered: Ar)- (xr+1 - })* + (%, – )* + (xr-1 -…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Related questions

Topic Video

Question

Explain to me how it became like this ???

1
LnPr,s
(Pr+1,s + Pr-1,s + Pr,s+1 + Pr,s-1 – 4P,,s)
|
(Ax)?
2
(xr+1 - }) + (v. - )?
+ (ys – )
+ (x,-1 -)°+ (y. –)*
+ (x, – )° + (y.+1 - )
+ (x, – ) + (y-1- )
-4 (r, – })° + (v. – })*)
2
2
1
(Ax)?
2
(x, + Ax – })²+ (ys – })*
2
2
+ (x, – Ar -) + (y. – })
1) 2
– })?
1
2
+ (x, – )´ + (ys + Ax
+ (x, – }) + (y. - Ar – })²
(Ar)²
12
|
(4, - })° + (y. – })*)
-4
4,
||

Expert Solution

Step 1

Given that,

$\begin{array}{rcl} L_{h} ϕ_{r, s} & = & \frac{1}{{(△ x)}^{2}} (ϕ_{r + 1, s} + ϕ_{r - 1, s} + ϕ_{r, s + 1} + ϕ_{r, s - 1} - 4 ϕ_{r, s}) \\ = & \frac{1}{{(△ x)}^{2}} ({(x_{r + 1} - \frac{1}{2})}^{2} + {(y_{s} - \frac{1}{2})}^{2} + {(x_{r - 1} - \frac{1}{2})}^{2} + {(y_{s} - \frac{1}{2})}^{2} + {(x_{r} - \frac{1}{2})}^{2} + {(y_{s + 1} - \frac{1}{2})}^{2} + {(x_{r} - \frac{1}{2})}^{2} + {(y_{s - 1} - \frac{1}{2})}^{2} - 4 ({(x_{r} - \frac{1}{2})}^{2} + {(y_{s} - \frac{1}{2})}^{2})) \end{array}$

Therefore, from the above equation,

$ϕ_{r, s} = \begin{array}{rcl} (x_{r} - \frac{1}{2}) \end{array} \begin{array}{rcl} \end{array}$ ²+ys-12²

Trending now

This is a popular solution!

Step by step

Solved in 4 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Research Design Formulation$

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.

Similar questions