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In numerical analysis, the Bulirsch–Stoer algorithm is a method for the numerical solution of ordinary differential equations which combines three powerful ideas: Richardson extrapolation, the use of rational function extrapolation in Richardson-type applications, and the modified midpoint method, [1] to obtain numerical solutions to ordinary ...
To find the depth of a rainfall of duration D and return period T at a given location in the UK, the following should be carried out: Find M5-60 minutes rainfall depth and "r" for the location using FSR maps. Divide this rainfall depth by "r" to get the M5-2 days depth. Multiply the M5-2 days depth by factor Z1 to find the M5-D depth.
Example 2: We can demonstrate the same methods on a more complex game and solve for the rational strategies. In this scenario, the blue coloring represents the dominating numbers in the particular strategy. Step-by-step solving: For Player 2, X is dominated by the mixed strategy 1 / 2 Y and 1 / 2 Z.
A number of methods can be used to calculate time of concentration, including the Kirpich (1940) [2] and NRCS (1997) [3] methods. Time of concentration is useful in predicting flow rates that would result from hypothetical storms, which are based on statistically derived return periods through IDF curves .
Like the sine, the cosine and tangent are replaced with rational equivalents, called the "cross" and "twist", and Divine Proportions develops various analogues of trigonometric identities involving these quantities, [3] including versions of the Pythagorean theorem, law of sines and law of cosines.
It is important to note that the gradually varied flow equations and associated numerical methods (including the standard step method) cannot accurately model the dynamics of a hydraulic jump. [6] See the Hydraulic jumps in rectangular channels page for more information. Below, an example problem will use conceptual models to build a surface ...
The rational planning model is a model of the planning process involving a number of rational actions or steps. Taylor (1998) outlines five steps, as follows: [ 1 ] Definition of the problems and/or goals;
For example, a quadratic for the numerator and a cubic for the denominator is identified as a quadratic/cubic rational function. The rational function model is a generalization of the polynomial model: rational function models contain polynomial models as a subset (i.e., the case when the denominator is a constant).