Write down the first four terms of the Taylor series expansion of the function x(t-h) about...

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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? 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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