Question: Denote Eulers method solution of the initial-value problem using step size h = 0.1 by X a (t), and that using h = 0.05 by

Denote Euler’s method solution of the initial-value problem

d.x dt xt 1 + 2 x(1) = 2

using step size h = 0.1 by X_a(t), and that using h = 0.05 by X_b(t). Find the values of X_a(2) and X_b(2). Estimate the error in the value of Xb(2), and suggest a value of step size that would provide a value of X(2) accurate to 0.1%. Find the value of X(2) using this step size. Find the exact solution of the initial-value problem, and determine the actual magnitude of the errors in X_a(2), X_b(2) and your final value of X(2).

d.x dt xt 1 + 2 x(1) = 2

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A suitable pseudocode program for computing the estimates X2 and X2 is the following procedure derivt x f fxt tt2 endprocedure tstart 1 xstart 2 tend 2 write vdu Enter stepsize read keyboard h write printer tstartxstart ttstart x xstart repeat deriv t x f tth x x hf write printer t x until t tend A Pascal implementation of the pseudocode program is the following program exercise41 var tstartxstart tend h x t f real procedure deriv ... View full answer

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