a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider the second-order truncation error (0(Ax )²) with the step size (-Ax ) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x ( Ux(x, t)).
a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is held cons. b) Consider the second-order truncation error (0(Ax )²) with the step size (-Ax ) and then, obtain a finite difference approximation for the first-order derivative of U(x, t) respect x ( Ux(x, t)).
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter9: Multivariable Calculus
Section9.CR: Chapter 9 Review
Problem 4CR
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Transcribed Image Text:a) Use the Taylor theorem for function U(x, t) with the step size(-Ax) (t, is
held cons.
b) Consider the second-order truncation error (O(Ax )²) with the step size
(-Ax ) and then, obtain a finite difference approximation for the first-order
derivative of U(x, 1) respect x ( Ux(x, t)).
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