Given the one-dimensional Poisson's equation d?V(x) dx? 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.

Given the one-dimensional Poisson's equation d?V(x) dx? 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

Section: Chapter Questions

Problem 1RQ

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.

Question

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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