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11 Nov 2019
Consider the differential equation dy / dx = 4x, with initial condition y(0) = 4. Use Euler's method with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) What is the solution to this differential equation (with the given initial condition)? Y = What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = By what factor should the error in these approximations change (that is: the error with two steps should be what number times the error with four)? Factor = (How close to this is the result you obtained above?)
Consider the differential equation dy / dx = 4x, with initial condition y(0) = 4. Use Euler's method with two steps to estimate y when x = 1: y(1) (Be sure not to round your calculations at each step!) Now use four steps: y(1) (Be sure not to round your calculations at each step!) What is the solution to this differential equation (with the given initial condition)? Y = What is the magnitude of the error in the two Euler approximations you found? Magnitude of error in Euler with 2 steps = Magnitude of error in Euler with 4 steps = By what factor should the error in these approximations change (that is: the error with two steps should be what number times the error with four)? Factor = (How close to this is the result you obtained above?)
Jarrod RobelLv2
3 Jul 2019