Given the one-dimensional Poisson's equation d²V(x) _ _ P dx2 Eo with p = 60€, and subject to boundary conditions of V(0) = 0V and V(1) = 5V, use the finite-difference technique to solve for the potential with Ax = 0.2. Determine the difference equation for V," where i is the grid point index and n is the iteration number. Plot the input and output for the given conditions.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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What are the values of V for the 5 iterations?

Given the one-dimensional Poisson's equation
d²V(x)
dx2
Eo
with p = 60€, and subject to boundary conditions of V(0) = 0V and V(1) = 5V, use the
finite-difference technique to solve for the potential with Ax = 0.2. Determine the
(n)
difference equation for V,") where i is the grid point index and n is the iteration
number. Plot the input and output for the given conditions.
Transcribed Image Text:Given the one-dimensional Poisson's equation d²V(x) dx2 Eo with p = 60€, and subject to boundary conditions of V(0) = 0V and V(1) = 5V, use the finite-difference technique to solve for the potential with Ax = 0.2. Determine the (n) difference equation for V,") where i is the grid point index and n is the iteration number. Plot the input and output for the given conditions.
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