Question: Denote Eulers method solution of the initial-value problem using step size h = 0.05 by Xa(t), and that using h = 0.025 by Xb(t). Find

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

d.x dt || 1 In x x(1) = 1.2

using step size h = 0.05 by Xa(t), and that using h = 0.025 by Xb(t). Find the values of X_a(1.5) and X_b(1.5). Estimate the error in the value of X_b(1.5), and suggest a value of step size that would provide a value of X(1.5) accurate to 0.25%. Find the value of X(1.5) using this step size. Find the exact solution of the initial-value problem, and determine the actual magnitude of the errors in X_a(1.5), X_b(1.5) and your final value of X(1.5).

d.x dt || 1 In x x(1) = 1.2

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