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  3. 3 given the initial value problem dx dtftx x0 ...

Question: 3 given the initial value problem dx dtftx x0 ...

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3. Given the initial value problem dx dt=f(t,x), x(0) = 20, 0<t where f is a continuous differentiable function that satisfies a Lipshitz condition. (a) Determine the coefficients in the following two-step linear multistep numerical method: where zn is an approximation of r(tn) and h is the time-step size, so it has as high an order of consistency as possible. What is its order of consistency and what is the error constant for the resulting method? (b) Is the resulting method convergent? Explain your result theoretically!
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