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Suppose: u(x, t) = x² + t², 0≤x≤ 1, 0st≤1, and consider Ax = 0.25, At = 0.5, then: Determine the coordinate of grid points. Approximate the U₂(x, t) and also U₁(x, t) by first order forward difference FD approximation, Approximate the U, (x, t) and also U₂(x, t) by first order backward difference FD approximation, d Approximate the U₂(x, t) and also U₂(x, t) by second order central difference FD approximation wengt)=xt oLKalyo

Suppose: u(x, t) = x² + t², 0≤x≤ 1, 0st≤1, and consider Ax = 0.25, At = 0.5, then: Determine the coordinate of grid points. Approximate the U₂(x, t) and also U₁(x, t) by first order forward difference FD approximation, Approximate the U, (x, t) and also U₂(x, t) by first order backward difference FD approximation, d Approximate the U₂(x, t) and also U₂(x, t) by second order central difference FD approximation wengt)=xt oLKalyo

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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Suppose: u(x, t) = x² + t², 0≤x≤ 1, 0st≤ 1, and consider Ax = 0.25, At = 0.5, then: Determine the coordinate of grid points. Approximate the U₂ (x, t) and also U, (x, t) by first order forward difference FD approximation, Approximate the U, (x, t) and also U₂(x, t) by first order backward difference FD approximation, Approximate the U, (x, t) and also U₂(x, t) by second order central difference FD approximation. e) Approximate the Uxx(x, t) and also U₁(x, t) by second order symmetr wert)=xt << < t <1 1
Transcribed Image Text:Suppose: u(x, t) = x² + t², 0≤x≤ 1, 0st≤ 1, and consider Ax = 0.25, At = 0.5, then: Determine the coordinate of grid points. Approximate the U₂ (x, t) and also U, (x, t) by first order forward difference FD approximation, Approximate the U, (x, t) and also U₂(x, t) by first order backward difference FD approximation, Approximate the U, (x, t) and also U₂(x, t) by second order central difference FD approximation. e) Approximate the Uxx(x, t) and also U₁(x, t) by second order symmetr wert)=xt << < t <1 1
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