Consider the hyperbolic partial derivative equation Uzz = Uu – sin (x), rE [0, 1], t>0, with the boundary and initial conditions u(0, t) = uz(1,t) = 0, t>0, u(x,0) = (x/2)(1 –- r), u(x,0) = 0, rE [0,1]. %3D (a) Transform the problem into an explicit finite difference scheme of order O(k2 +h?).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Consider the hyperbolic partial derivative equation
Uzz = Uu – sin (x), rE [0, 1), t>0,
with the boundary and initial conditions
u(0, t) = uz(1, t) 0, t> 0,
u(x, 0) = (x/2)(1 – x), u(x,0) = 0, r E [0, 1].
%3D
(a) Transform the problem into an explicit finite difference scheme of order
(4+ Y)O
Transcribed Image Text:Consider the hyperbolic partial derivative equation Uzz = Uu – sin (x), rE [0, 1), t>0, with the boundary and initial conditions u(0, t) = uz(1, t) 0, t> 0, u(x, 0) = (x/2)(1 – x), u(x,0) = 0, r E [0, 1]. %3D (a) Transform the problem into an explicit finite difference scheme of order (4+ Y)O
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