For the following questions use h = 0.2. Also, clearly state all the values for xi’s and yi’s you would be using before each iteration. Adams-Bashforth Two-Step Method yi+1 =yi+(h/2) [3f(xi,yi)−f(xi−1,yi−1)] where i = 1, 2, ....N − 1. The local error is O(h^3) For the Adams-Bashforth two-step explicit method, use the Euler and the Trapezium rule as a predictor-corrector method with two iterations to obtain a starter value for y1. Use the Taylor series method with the appropriate number of terms to obtain another starter value for y1. For the above values for y1 compare with the exact value and comment on your result for each iteration. With your most accurate value for y1 found above, use the Adams- Bashforth Two-Step method to find the approximate value for the given differential equation at y2. Adams-Bashforth Three-Step Method yi+1 =yi + (h/12) [23f(xi,yi)−16f(xi−1,yi−1)+5f(xi−2,yi−2)] where i = 2, 3, ....N − 1. The local error is O(h^4) By using the exact value for y2, use the Adams-Bashforth three-step method to find y3.

Question

For the following questions use h = 0.2. Also, clearly state all the values for xi’s and yi’s you would be using before each iteration.

Adams-Bashforth Two-Step Method

yi+1 =yi+(h/2) [3f(xi,yi)−f(xi−1,yi−1)] where i = 1, 2, ....N − 1. The local error is O(h^3)

For the Adams-Bashforth two-step explicit method, use the Euler and the Trapezium rule as a predictor-corrector method with two iterations to obtain a starter value for y1.
Use the Taylor series method with the appropriate number of terms to obtain another starter value for y1.

For the above values for y1 compare with the exact value and comment on your result for each iteration.
With your most accurate value for y1 found above, use the Adams- Bashforth Two-Step method to find the approximate value for the given differential equation at y2.

Adams-Bashforth Three-Step Method

yi+1 =yi + (h/12) [23f(xi,yi)−16f(xi−1,yi−1)+5f(xi−2,yi−2)]

where i = 2, 3, ....N − 1. The local error is O(h^4)