A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x' and its two ends are embedded in ice at temperature zero. Consider the partial differential equation where: u, (x,t) = 5u „ (x,t), for 0 0 with the initial condition: u(x,0) = f(x) = 2x³ for 0

A copper rod 1 cm long with insulated lateral surface has initial temperature function, f(x) = 2x' and its two ends are embedded in ice at temperature zero. Consider the partial differential equation where: u, (x,t) = 5u „ (x,t), for 0 0 with the initial condition: u(x,0) = f(x) = 2x³ for 0

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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Step by step solution

A copper rod 1 cm long with insulated lateral surface has initial temperature function,
f(x) = 2x and its two ends are embedded in ice at temperature zero. Consider the
partial differential equation where:
u, (x,t) = 5u (x,1), for 0<x<1, t > 0
with the initial condition:
u(x,0) = f(x) = 2x° for 0<x<1
and the boundary conditions:
u(0,t) = 0, for 0st<0.10
u(1,t) = 2, for 0s150.10
(a)
Show whether the partial differential equation is hyperbolic, parabolic or elliptic.
(b)
Describe graphically and explain how four points are used to generate the finite
difference formula for heat equation.
(c)
Solve u(x,t) numerically with h= 0.2 and k =0.05.

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