Direct Method


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Direct Method

 

in mathematics, a type of method for the solution of problems of mathematical analysis. Usually classed as direct methods are methods for solving, for example, differential equations, integral equations, integro-differential equations, and variational problems by means of the construction of a sequence of functions (or systems of functions) that converge to the solution of a simpler problem; this simpler problem generally, in the limit, coincides with the given problem. Direct methods are used most often for the approximate solution of problems in mathematical analysis. They are sometimes also used to find exact solutions and to prove existence theorems for solutions.

Examples of direct methods are finite-difference methods for solving differential, integral, and integro-differential equations; the Euler method for solving problems in the calculus of variations; the Ritz method and the method of steepest descents, which are used to solve variational problems and problems that reduce to variational problems; and the Galerkin method, which is used to solve many boundary-value problems, including those that do not reduce to variational problems.

References in periodicals archive ?
Static and fatigue analysis made on an ultrasonic horn used for cavitation erosion tests on vibratory systems by direct method, confirmed the conclusion resulting from experimental research: the emergence of a fatigue fracture after a number of cycles that was lower than expected for this type of components.
58 shows that the equilibrium equation with the direct method was not able to estimate exactly the amount of bacterial movement in soil (Fig 2-A).
The direct method that is based on line-source approximation (Gehlin, 2002) is simpler, and has thus gained greater acceptance.
Most of these studies suggested that the direct method tends to produce greater CO scores than the indirect method (Otten & van der Pligt, 1996; Spitzenstetter, 2003), except for the study conducted by Welkenhuysen, Evers-Kiebooms, Decruyenaere, and van den Berghe (1996), which suggested that the indirect method may induce more CO than the direct method.
The most direct method is to set up a rogue access point and then use an iFrame to direct the user to a Google service (such as Alerts) that doesn't use an encrypted channel, they said.
In the direct Method for the Study and Optimization of Irreversible Cycles with Finite Speed, equations based on the first law of thermodynamics for Processes with finite Speed are integrated in such a manner that the expressions for efficiency and power are obtained directly for any irreversible Cycle.
For the first time, a direct method is now available that uses conventional blood samples to detect doping via gene transfer and is still effective if the actual doping took place up to 56 days before," Professor Perikles Simon, MD, PhD from Johannes Gutenberg University Mainz, Germany explained.
For pedagogy, our findings can provide better understanding of nonarticulation in the SCF, leading to a deeper discussion of the issue of the direct method versus the indirect method.
They describe mathematical models governing the stability of fluid flows, incompressible Navier-Stokes fluid, elements of calculus variations, variants of the energy method for non-stationary equations, applications to linear Benard convections, variational methods applied to linear stability, and applications of the direct method to linear stability.
Since V is a positive definite function and V is a negative definite function, according to the Lyapunov's direct method, the system (1) and system (2) achieve the projective synchronization under the controller (3).
The proposal would also mandate the use of the direct method for presenting cash flows, as well as include a new schedule in the notes of the financial statement that reconciles cash flow to comprehensive income.

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