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  2. Quintic function - Wikipedia

    en.wikipedia.org/wiki/Quintic_function

    Because they have an odd degree, normal quintic functions appear similar to normal cubic functions when graphed, except they may possess one additional local maximum and one additional local minimum. The derivative of a quintic function is a quartic function. Setting g(x) = 0 and assuming a ≠ 0 produces a quintic equation of the form:

  3. Runge–Kutta–Fehlberg method - Wikipedia

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

    "Approximate Solution of Ordinary Differential Equations and Their Systems Through Discrete and Continuous Embedded Runge-Kutta Formulae and Upgrading Their Order". Computers & Mathematics with Applications .

  4. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    The consequence of this difference is that at every step, a system of algebraic equations has to be solved. This increases the computational cost considerably. If a method with s stages is used to solve a differential equation with m components, then the system of algebraic equations has ms components.

  5. Numerical methods for ordinary differential equations - Wikipedia

    en.wikipedia.org/wiki/Numerical_methods_for...

    In a BVP, one defines values, or components of the solution y at more than one point. Because of this, different methods need to be used to solve BVPs. For example, the shooting method (and its variants) or global methods like finite differences, [3] Galerkin methods, [4] or collocation methods are appropriate for that class of problems.

  6. List of Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/List_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.

  7. Abel–Ruffini theorem - Wikipedia

    en.wikipedia.org/wiki/Abel–Ruffini_theorem

    Polynomial equations of degree two can be solved with the quadratic formula, which has been known since antiquity. Similarly the cubic formula for degree three, and the quartic formula for degree four, were found during the 16th century. At that time a fundamental problem was whether equations of higher degree could be solved in a similar way.

  8. Finite difference method - Wikipedia

    en.wikipedia.org/wiki/Finite_difference_method

    For example, consider the ordinary differential equation ′ = + The Euler method for solving this equation uses the finite difference quotient (+) ′ to approximate the differential equation by first substituting it for u'(x) then applying a little algebra (multiplying both sides by h, and then adding u(x) to both sides) to get (+) + (() +).

  9. Variational inequality - Wikipedia

    en.wikipedia.org/wiki/Variational_inequality

    Following Antman (1983, p. 283), the definition of a variational inequality is the following one.. Given a Banach space, a subset of , and a functional : from to the dual space of the space , the variational inequality problem is the problem of solving for the variable belonging to the following inequality: