Adam-Moulton method or order 3 is a:Question 4Answera.3rd order explicit methodb. 3rd order implicit methodc.None of these

The Adam-Moulton method is a type of multistep method used for solving ordinary differential equations (ODEs). Specifically, the 3rd order Adam-Moulton method is classified as an implicit method because it requires the evaluation of the function at the next time step, which encapsulates the unknown values for the current iteration.

1. Break Down the Problem

   • Identify what Adam-Moulton method is and its nature (explicit vs. implicit).
   • Determine the order of the method in question.

2. Relevant Concepts

   • The Adam-Moulton methods are designed to be implicit integration schemes, meaning they typically require solving equations that involve the function's value at the next time step, making them more stable in certain scenarios compared to explicit methods.

3. Analysis and Detail

   • The 3rd order Adam-Moulton method uses previous estimates to approximate future values and necessitates that the values of unknowns be located at the new step, thus fitting the implicit classification.

4. Verify and Summarize

   • In summary, the correct classification of the 3rd order Adam-Moulton method is that it is an implicit method as it relies on future knowledge to proceed through each step.

Final Answer

The correct answer is b. 3rd order implicit method.