(a) Replace the so-called two-term Taylor estimate (equation (8) in Problem 23) by the three-term result: Compute...
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Compute the second derivative y" in terms of f, and fy (partial derivatives of f, with respect to t and y, respectively), and deduce the three-term Taylor approximation:
(b) Show that the local discretization error en+l in this scheme is O(h3).
(c) Apply the method t o the I V P i n Problem 1 and compare the results.
(d) Repeat (c) for Problem 2.
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Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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