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  2. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    The numerical solution to the linear test equation decays to zero if | r(z) | < 1 with z = hλ. The set of such z is called the domain of absolute stability. In particular, the method is said to be absolute stable if all z with Re(z) < 0 are in the domain of absolute stability. The stability function of an explicit Runge–Kutta method is a ...

  3. Runge–Kutta–Fehlberg method - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta–Fehlberg...

    The solution is the weighted average of six increments, where each increment is the product of the size of the interval, , and an estimated slope specified by function f on the right-hand side of the differential equation.

  4. Heun's method - Wikipedia

    en.wikipedia.org/wiki/Heun's_method

    It is named after Karl Heun and is a numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. Both variants can be seen as extensions of the Euler method into two-stage second-order Runge–Kutta methods. The procedure for calculating the numerical solution to the initial value problem:

  5. Absolute value - Wikipedia

    en.wikipedia.org/wiki/Absolute_value

    The real absolute value function is an example of a continuous function that achieves a global minimum where the derivative does not exist. The subdifferential of | x | at x = 0 is the interval [−1, 1]. [14] The complex absolute value function is continuous everywhere but complex differentiable nowhere because it violates the Cauchy–Riemann ...

  6. Absolute value (algebra) - Wikipedia

    en.wikipedia.org/wiki/Absolute_value_(algebra)

    The standard absolute value on the integers. The standard absolute value on the complex numbers.; The p-adic absolute value on the rational numbers.; If R is the field of rational functions over a field F and () is a fixed irreducible polynomial over F, then the following defines an absolute value on R: for () in R define | | to be , where () = () and ((), ()) = = ((), ()).

  7. Linear multistep method - Wikipedia

    en.wikipedia.org/wiki/Linear_multistep_method

    Iterative methods such as Newton's method are often used to solve the implicit formula. Sometimes an explicit multistep method is used to "predict" the value of +. That value is then used in an implicit formula to "correct" the value. The result is a predictor–corrector method.

  8. Geometrical properties of polynomial roots - Wikipedia

    en.wikipedia.org/wiki/Geometrical_properties_of...

    takes a negative value for some positive real value of x. In the remaining of the section, suppose that a 0 ≠ 0. If it is not the case, zero is a root, and the localization of the other roots may be studied by dividing the polynomial by a power of the indeterminate, getting a polynomial with a nonzero constant term.

  9. Ostrowski's theorem - Wikipedia

    en.wikipedia.org/wiki/Ostrowski's_theorem

    The real absolute value on the rationals is the standard absolute ... In other words, the absolute value of a negative integer coincides with that of its opposite.