Consider the differential equation dy =x²²e-* - y dx (1) with the initial conditions x = 0, y = 1. For the remainder of this question work to 4 decimal places throughout and give your answer to 3 decimal places. (a) Use the Euler method to calculate an estimate of the value of y when x = 0.8 using the step length h 0.2. = (b) Use the Modified Euler method to calculate an estimate of the value of y when x = 0.8 using the step length h = 0.4. (c) Use the RK4 method to calculate an estimate of the value of y when x = 0.8 using the step length h= 0.4. (d) The exact solution to the differential equation (1) is y(x) = - (₁ Check that this function indeed satisfies equation (1) together with the initial condition: y = 1 when x 0. Then evaluate the value predicted by the exact solution when x=0.8. (e) Compare the value you found in part (d) with the estimated values you found in parts (a), (b) and (c). State which method gives the most accurate prediction and which method gives the least accurate prediction

Consider the differential equation dy =x²²e-* - y dx (1) with the initial conditions x = 0, y = 1. For the remainder of this question work to 4 decimal places throughout and give your answer to 3 decimal places. (a) Use the Euler method to calculate an estimate of the value of y when x = 0.8 using the step length h 0.2. = (b) Use the Modified Euler method to calculate an estimate of the value of y when x = 0.8 using the step length h = 0.4. (c) Use the RK4 method to calculate an estimate of the value of y when x = 0.8 using the step length h= 0.4. (d) The exact solution to the differential equation (1) is y(x) = - (₁ Check that this function indeed satisfies equation (1) together with the initial condition: y = 1 when x 0. Then evaluate the value predicted by the exact solution when x=0.8. (e) Compare the value you found in part (d) with the estimated values you found in parts (a), (b) and (c). State which method gives the most accurate prediction and which method gives the least accurate prediction

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.3: Euler's Method

Problem 22E

See similar textbooks