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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.
An implicit data structure is one with constant O(1) space overhead (above the information-theoretic lower bound).. Historically, Munro & Suwanda (1980) defined an implicit data structure (and algorithms acting on one) as one "in which structural information is implicit in the way data are stored, rather than explicit in pointers."
In the study of graph algorithms, an implicit graph representation (or more simply implicit graph) is a graph whose vertices or edges are not represented as explicit objects in a computer's memory, but rather are determined algorithmically from some other input, for example a computable function.
But even without specifying this explicit solution, it is possible to refer to the implicit solution of the unit circle equation as y = f(x), where f is the multi-valued implicit function. While explicit solutions can be found for equations that are quadratic, cubic, and quartic in y, the same is not in general true for quintic and higher ...
In numerical analysis, the Runge–Kutta methods (English: / ˈ r ʊ ŋ ə ˈ k ʊ t ɑː / ⓘ RUUNG-ə-KUUT-tah [1]) are a family of implicit and explicit iterative methods, which include the Euler method, used in temporal discretization for the approximate solutions of simultaneous nonlinear equations. [2]
For larger time steps, the implicit scheme works better since it is less computationally demanding. The explicit scheme is the least accurate and can be unstable, but is also the easiest to implement and the least numerically intensive. Here is an example.
In mathematics, an implicit curve is a plane curve defined by an implicit equation relating two coordinate variables, commonly x and y. For example, the unit circle is defined by the implicit equation x 2 + y 2 = 1 {\displaystyle x^{2}+y^{2}=1} .
Tacit knowledge or implicit knowledge is knowledge that is difficult to extract or articulate—as opposed to conceptualized, formalized, codified, or explicit knowledge—is more difficult to convey to others through verbalization or writing.