Implicit Solvers

Implicit solvers are numerical methods for solving systems of equations where the solution variables are not explicitly given in terms of the input variables. In other words, the equations are not in a form that allows for a direct solution of the variables. Implicit solvers differ from explicit solvers in that they do not require an explicit formula for the solution at each time step.

Instead, implicit solvers use an iterative numerical method to solve the system of equations. This involves guessing an initial solution and then iterating towards a more accurate solution until a convergence criterion is met. This iterative process can be computationally expensive, but it allows for the solution of more complex systems of equations than explicit solvers.

Implicit solvers are commonly used in numerical simulations of physical systems, such as fluid dynamics, where the equations are often non-linear and difficult to solve analytically. They are also used in financial modeling, such as in option pricing, where the equations are often stochastic and involve partial differential equations.