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You are given the differential equation dy/dx = y' = f(x, y) with initial condition y(0 ) 1 = . The following numerical method is also given:
where fn = f( xn , yn) = f(nh, yn) x , y f nh, y = = and h is the integration step.
(a) Is this an explicit or implicit method? Explain you answer.
(b) Find an expression for local error of this method.
(c) If one takes f = - σy (where σ > 0 and constant) is this method stable? Prove your answer mathematically.
(d) What is the condition for the iterative convergence of the method (when f = - σy )? Show that fulfillment of the condition for stability of the method assures iterative convergence.
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a b c d e supply p 3 4 6 8 8 20 q 2 6 0 5 8 30 r 7 11 20 40 3 15 s 1 0 9 14 6 13 d 15 3 12 10 20
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