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e 1 Use steps sizes (a) h = 0.1 and k = 0.0005 and (b) h = 0.1 and k = 0.01 to approximate the solution to the heat equation ди 22 и -(x, t) at √x²(x,t) = 0, 0 < x <1, 0≤t, with boundary conditions u(0,t) = u(1,t) = 0, 0

e 1 Use steps sizes (a) h = 0.1 and k = 0.0005 and (b) h = 0.1 and k = 0.01 to approximate the solution to the heat equation ди 22 и -(x, t) at √x²(x,t) = 0, 0 < x <1, 0≤t, with boundary conditions u(0,t) = u(1,t) = 0, 0

Advanced Engineering Mathematics
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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e 1 Use steps sizes (a) h = 0.1 and k = 0.0005 and (b) h = 0.1 and k = 0.01 to approximate the solution to the heat equation ди 22 и -(x, t) at √x²(x,t) = 0, 0 < x <1, 0≤t, with boundary conditions u(0,t) = u(1,t) = 0, 0 <t, and initial conditions u(x, 0) = sin(x), 0≤x≤1. Compare the results at t=0.5 to the exact solution u(x,t) = e−π²+ sin(x).
Transcribed Image Text:e 1 Use steps sizes (a) h = 0.1 and k = 0.0005 and (b) h = 0.1 and k = 0.01 to approximate the solution to the heat equation ди 22 и -(x, t) at √x²(x,t) = 0, 0 < x <1, 0≤t, with boundary conditions u(0,t) = u(1,t) = 0, 0 <t, and initial conditions u(x, 0) = sin(x), 0≤x≤1. Compare the results at t=0.5 to the exact solution u(x,t) = e−π²+ sin(x).
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