Consider the initial-value problem y' = 2x - 3y + 1, y(1) = 7. The analytic solution is y(x)-공 + 글x + 홍 ㅇ e-3(x - 1). (a) Find a formula involving c and h for the local truncation error in the nth step Euler's method is used. (b) Find a bound for the local truncation error in each step if h = 0.1 is used to approximate y(1.5). (Proceed as in Example 1 of Section 6.1.) (c) Approximate y(1.5) using h = 0.1 and h = 0.05 with Euler's method. See Problem 1 in Exercises 2.6. (Round your answers to four decimal places.) h = 0.1 y(1.5) = y(1.5) = h = 0.05 (d) Calculate the errors in part (c) and verify that the global truncation error of Euler's method is O(h). (Round your answers to four decimal places.) the error forh 0.1 is Eo.1 = |, while the error for h = 0.05 is Eo.05 = Since y(1.5) = Eo.1/Eo.05 * 2. We actually have Eo.1/Eo.05 = With global truncation error O(h) we expect (rounded to two decimal places).

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.