Sample interview questions: Explain the difference between explicit and implicit numerical methods.
Sample answer:
Explicit Methods:
- Description:
- Explicit numerical methods directly calculate the solution at a new time step using values from the previous time step.
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They explicitly express the new solution in terms of the known values.
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Advantages:
- Simple to implement: Explicit methods are straightforward to program and can be easily parallelized.
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Efficient for small time steps: When the time step is small, explicit methods can be very efficient.
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Disadvantages:
- Stability restrictions: Explicit methods often have stability restrictions that limit the size of the time step that can be used. If the time step is too large, the method may become unstable and produce incorrect results.
- Accuracy limitations: Explicit methods are generally less accurate than implicit methods, especially for stiff systems.
Implicit Methods:
- Description:
- Implicit numerical methods solve a system of equations to determine the solution at the new time step.
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They involve an iterative process to compute the solution, which is implicitly defined by the equations.
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Advantages:
- Stability: Implicit methods are generally more stable than explicit methods, allowing for larger … Read full answer
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