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In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German mathematician Erwin Fehlberg and is based on the large class of Runge–Kutta methods .
Diagonally Implicit Runge–Kutta (DIRK) formulae have been widely used for the numerical solution of stiff initial value problems; [6] the advantage of this approach is that here the solution may be found sequentially as opposed to simultaneously. The simplest method from this class is the order 2 implicit midpoint method.
The limit, should it exist, is a positive real solution of the equation y = x y. Thus, x = y 1/y. The limit defining the infinite exponential of x does not exist when x > e 1/e because the maximum of y 1/y is e 1/e. The limit also fails to exist when 0 < x < e −e. This may be extended to complex numbers z with the definition:
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]
Measurements, first and second derivative in a potentiometric titration. In analytical chemistry, potentiometric titration is a technique similar to direct titration of a redox reaction. It is a useful means of characterizing an acid. No indicator is used; instead the electric potential is measured across the analyte, typically an electrolyte ...
The volumetric titration is based on the same principles as the coulometric titration, except that the anode solution above now is used as the titrant solution. The titrant consists of an alcohol (ROH), base (B), SO 2 and a known concentration of I 2. Pyridine has been used as the base in this case. One mole of I 2 is consumed for each mole of ...
Iodometry, known as iodometric titration, is a method of volumetric chemical analysis, a redox titration where the appearance or disappearance of elementary iodine indicates the end point. Note that iodometry involves indirect titration of iodine liberated by reaction with the analyte, whereas iodimetry involves direct titration using iodine as ...
Complexometric titrations are particularly useful for the determination of a mixture of different metal ions in solution. An indicator capable of producing an unambiguous color change is usually used to detect the end-point of the titration. Complexometric titrations are those reactions where a simple ion is transformed into a complex ion and ...