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d) An alternative to the two above methods are as follows. Suppose we solve x ?=

ID: 3758869 • Letter: D

Question

d) An alternative to the two above methods are as follows. Suppose we solve x ?= f (t, x). The new method s based on that the step of approach (tk. XK. ) to approach (tk + 1, Xk+1) s calculated by X k+1 = + h f( tk + h /2, (Xk+1 + Xk )/2 For the equation (1) gives Xk+1 = + h (1 +((Xk+xk.1)2/ 4) (2) This equation can be solved with respect to Xk+1, which gives Xk+1 (2-hXk -2sqrt(1-h^2Xh)/h (3) Create an algorithm that calculates Xk+1 using this formula. Are there any restrictions on what h that can be used? Makes 6 steps as for the other methods, and add also this solution into the same plot as the other solutions. Which method seems to work. best?

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