Question
Write down the first four terms of the Taylor series expansion of the function x(t-h) about x(t), and the first three terms of the
Write down the first four terms of the Taylor series expansion of the function x(t-h) about x(t), and the first three terms of the expansion of the function dx (t-h) dt about x(t). Use these two equations to eliminate dt (1) and dt (1) from the Taylor series expansion of the function x(t + h) about x(t). Show that the resulting formula is Xn+1 = -4X +5Xn-1 + h(4F + 2F-1) + 0(h*) Show that this method is a linear combination of the second-order Adams-Bashforth method and the central difference method (that is, the scheme based on (2.9)). What do you think, in view of this, might be its disadvantages?
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A First Course in Differential Equations with Modeling Applications
Authors: Dennis G. Zill
10th edition
978-1111827052
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