Adams-Bashforth and Adam-Moulton

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In summary, when using the Adams-Bashforth method as a predictor and Adams-Moulton method as a corrector, after finding y_n+1 using the corrector method, it is necessary to re-calculate y'_n+1 in order to find y_n+2. This is because in the second integration step, the answer from the first step should be used, not an earlier guess at the answer. However, if the equation only depends on t and not on y, there may be no difference between the two values.
  • #1
johnchau123
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Hi,
I am doing a question on using Adams-Bashforth method as predictor and Adams-Moulton method as corrector.
I would like to ask after we find y_n+1 by corrector method, do we have to re-calculate y'_n+1 in order to find y_n+2, or we use the y'_n+1 originally found by the predicator method to find y_n+2 in corrector?

Thanks.
:smile:
 
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  • #2
Yes you do.

When you to the second integration step, you want to use "the answer" from the first step, not an earlier guess at the answer.

Of course if it happens that in your equation dy/dt = f(y,t), f only depends of t and not on y, there may be no difference between the two values.
 

1. What is the Adams-Bashforth method?

The Adams-Bashforth method is a numerical method used for solving ordinary differential equations. It is an explicit method, meaning that the solution is calculated using only previously known values. It is a multi-step method, meaning that it uses multiple previous values to calculate the next value in the solution.

2. How does the Adams-Bashforth method work?

The Adams-Bashforth method works by using a polynomial approximation to the solution of the differential equation. The coefficients of the polynomial are determined by using the previous values of the solution. These coefficients are then used to calculate the next value in the solution.

3. What are the advantages of using Adams-Bashforth method?

One advantage of using the Adams-Bashforth method is that it is relatively simple to implement and requires minimal computational effort. It also has a high order of accuracy, meaning that it can provide more accurate solutions compared to other numerical methods.

4. What are the limitations of the Adams-Bashforth method?

One limitation of the Adams-Bashforth method is that it can be unstable for certain types of differential equations, particularly those with oscillatory solutions. It also requires a large number of previous values to be accurate, making it less efficient for some problems.

5. What is the difference between Adams-Bashforth and Adams-Moulton methods?

The Adams-Moulton method is an implicit method, meaning that it uses both previous and current values to calculate the next value in the solution. This makes it more stable for certain types of differential equations, but also more computationally expensive. Additionally, the Adams-Moulton method can have a higher order of accuracy compared to Adams-Bashforth method.

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