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- Explicit_and_implicit_methods abstract "Explicit and implicit methods are approaches used in numerical analysis for obtaining numerical solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes.Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one. Mathematically, if is the current system state and is the state at the later time (is a small time step), then, for an explicit method while for an implicit method one solves an equation to find It is clear that implicit methods require an extra computation (solving the above equation), and they can be much harder to implement. Implicit methods are used because many problems arising in practice are stiff, for which the use of an explicit method requires impractically small time steps to keep the error in the result bounded (see numerical stability). For such problems, to achieve given accuracy, it takes much less computational time to use an implicit method with larger time steps, even taking into account that one needs to solve an equation of the form (1) at each time step. That said, whether one should use an explicit or implicit method depends upon the problem to be solved.".
- Explicit_and_implicit_methods wikiPageID "3652485".
- Explicit_and_implicit_methods wikiPageRevisionID "603271183".
- Explicit_and_implicit_methods hasPhotoCollection Explicit_and_implicit_methods.
- Explicit_and_implicit_methods subject Category:Numerical_differential_equations.
- Explicit_and_implicit_methods comment "Explicit and implicit methods are approaches used in numerical analysis for obtaining numerical solutions of time-dependent ordinary and partial differential equations, as is required in computer simulations of physical processes.Explicit methods calculate the state of a system at a later time from the state of the system at the current time, while implicit methods find a solution by solving an equation involving both the current state of the system and the later one.".
- Explicit_and_implicit_methods label "Explicit and implicit methods".
- Explicit_and_implicit_methods label "Métodos explícitos e implícitos".
- Explicit_and_implicit_methods sameAs Métodos_explícitos_e_implícitos.
- Explicit_and_implicit_methods sameAs m.09sd2v.
- Explicit_and_implicit_methods sameAs Q5421265.
- Explicit_and_implicit_methods sameAs Q5421265.
- Explicit_and_implicit_methods wasDerivedFrom Explicit_and_implicit_methods?oldid=603271183.
- Explicit_and_implicit_methods isPrimaryTopicOf Explicit_and_implicit_methods.