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# Two-Step and Four-Step Adams Predictor-Corrector Method

Consider the initial value problem , with . This Demonstration uses the two-step and four-step Adams predictor-corrector method to find the estimated solution of this first-order ordinary differential equation. In addition, the relative error is calculated for selected values of , where (i.e., we compare Adams method's solution with the result obtained using NDSolve, ). Finally, the Euclidean norm of the absolute error vector is given (i.e., ).

### DETAILS

The predictor-corrector method is a two-step technique. First, the prediction step calculates a rough approximation of the desired quantity, typically using an explicit method. Second, the corrector step refines the initial approximation in another way, typically with an implicit method.
(predictor step)
(corrector step)
The two-step and four-step Adams methods require two and four initial values to start the calculation, respectively. These later can be obtained by using other methods, for example Euler or Runge–Kutta.

### PERMANENT CITATION

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