Question: QUESTION 1 (a) Use the modified Euler method with At = 1 to solve the equation dy dt = ty, > (0) = 1 at

QUESTION 1 (a) Use the modified Euler method with At = 1 to solve the equation dy dt = ty, > (0) = 1 at t = 1. Re-correct until the change between two successive corrected values is less than 0.1. (6) (b) Use the third-order Taylor method with Ax = 0.1, to solve the differential equation dy = y, y(0) =1 dx at x = 0.1 and x = 0.2. (5) (c) (i) What is the main advantage of the modified Euler method over the simple Euler method? (ii) What is the main advantage of the modified Euler method over the second-order Taylor method? (5) (d) Give the orders of the local error and the global error of the modified Euler method. (2) [18]

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