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(a) Program a calculator or computer to use Euler s method to compute y(1) where y(x)is the solution of the initial-value problem
dy/dx + 3x2y = 6x2 y(0) = 3
(i) h = 1
(ii) h = 0.1
(iii) h = 0.01
(iv) h = 0.001
(b) Verify that y = 2 + e-x3 is is the exact solution of the differential equation.
(c) Find the errors in using Euler s method to compute y(1) with the step sizes in part (a). What happens to the error when the step size is divided by 10? |
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