Implicit and explicit methods have the same differences no matter what context. The building blocks from which these methods are constructed are the same, they all use Taylor series expansion of a function. Of course, there are many different numerical methods, explicit and implicit, with different degrees of numerical accuracy, consistency and stability.

The choice of using implicit or explicit methods is really dependent on the scales involved, the type of accuracy desired, etc. But in all practical terms, the most important factor is computational cost. Although implicit methods are unconditionally stable, they are very costly compared to explicit methods. To try to address some of those issues, a lot of atmospheric and oceanic solvers employ hybrid methods. These are called semi-implicit methods where some terms are implicit and others are explicit in order to reduce the computer time required to solve the equations.

Essentially, if time accuracy is important, explicit methods are more accurate and less computationally expensive. On the other hand, if the goal is forecasting to a reasonable degree of accuracy then an implicit method is best because, even though it is computationally expensive, one can use very large time steps and get to the answer quickly.

Implicit and explicit methods have the same differences no matter what context. The building blocks from which these methods are constructed are the same, they all use Taylor series expansion of a function. Of course, there are many different numerical methods, explicit and implicit, with different degrees of numerical accuracy, consistency and stability.

The choice of using implicit or explicit methods is really dependent on the scales involved, the type of accuracy desired, etc. But practically speaking, the most important factor is computational cost. Although implicit methods are unconditionally stable, they are very costly compared to explicit methods. To try to address some of those issues, a lot of atmospheric and oceanic solvers employ hybrid methods. These are called semi-implicit methods where some terms are implicit and others are explicit in order to reduce the computer time required to solve the equations.

Essentially, if time accuracy is important, explicit methods are more accurate and less computationally expensive. On the other hand, if the goal is forecasting to a reasonable degree of accuracy then an implicit method is best because, even though it is computationally expensive, one can use very large time steps and get to the answer quickly.

Implicit and explicit methods have the same differences no matter what context. The building blocks from which these methods are constructed are the same, they all use Taylor series expansion of a function. Of course, there are many different numerical methods, explicit and implicit, with different degrees of numerical accuracy, consistency and stability.

The choice of using implicit or explicit methods is really dependent on the scales involved, the type of accuracy desired, etc. But in all practical terms, the most important factor is computational cost. Although implicit methods are unconditionally stable, they are very costly compared to explicit methods. To try to address some of those issues, a lot of atmospheric and oceanic models employ hybrid methods. These are called semi-implicit methods where some terms are implicit and others are explicit in order to reduce the computer time required to solve the equations.

Essentially, if time accuracy is important, explicit methods are more accurate and less computationally expensive. On the other hand, if the goal is forecasting to a reasonable degree of accuracy then an implicit method is best because, even though it is computationally expensive, one can use very large time steps and get to the answer quickly.

Implicit and explicit methods have the same differences no matter what context. The building blocks from which these methods are constructed are the same, they all use Taylor series expansion of a function. Of course, there are many different numerical methods, explicit and implicit, with different degrees of numerical accuracy, consistency and stability.

The choice of using implicit or explicit methods is really dependent on the scales involved, the type of accuracy desired, etc. But in all practical terms, the most important factor is computational cost. Although implicit methods are unconditionally stable, they are very costly compared to explicit methods. To try to address some of those issues, a lot of atmospheric and oceanic solvers employ hybrid methods. These are called semi-implicit methods where some terms are implicit and others are explicit in order to reduce the computer time required to solve the equations.

Essentially, if time accuracy is important, explicit methods are more accurate and less computationally expensive. On the other hand, if the goal is forecasting to a reasonable degree of accuracy then an implicit method is best because, even though it is computationally expensive, one can use very large time steps and get to the answer quickly.