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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 .
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 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 solution.
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]
A titration curve is a curve in graph the x-coordinate of which represents the volume of titrant added since the beginning of the titration, and the y-coordinate of which represents the concentration of the analyte at the corresponding stage of the titration (in an acid–base titration, the y-coordinate usually represents the pH of the solution).
Standard solutions are generally prepared by dissolving a solute of known mass into a solvent to a precise volume, or by diluting a solution of known concentration with more solvent. [1] A standard solution ideally has a high degree of purity and is stable enough that the concentration can be accurately measured after a long shelf time. [2]
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 ...
A typical titration curve of a diprotic acid, oxalic acid, titrated with a strong base, sodium hydroxide.Both equivalence points are visible. Titrations are often recorded on graphs called titration curves, which generally contain the volume of the titrant as the independent variable and the pH of the solution as the dependent variable (because it changes depending on the composition of the ...