Chapter 5we obtain a system in normal formx01=x2,x02=x3,x03=x4+t,x04=x5,x05=15(2x4−2x3+1)with initial conditionsx1(0) =x2(0) =x3(0) = 4,x4(0) =x5(0) = 1.9.To see how the improved Euler’s method can be extended let’s recall, from Section 3.6, theimproved Euler’s method (pages 127–128 of the text). For the initial value problemx0=f(t, x)(t0)=x0,the recursive formulas for the improved Euler’s method aretn+1=tn+h,xn+1=xn+h2[f(tnn)+f(tn+h, xn+hf(tnn))],wherehis the step size. Now suppose we want to approximate the solutionx1(t),x2(t)tothesystemx01=f1(t, x12)an
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