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  2. Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/Runge–Kutta_methods

    Here + is the RK4 approximation of (+), and the next value (+) is determined by the present value plus the weighted average of four increments, where each increment is the product of the size of the interval, h, and an estimated slope specified by function f on the right-hand side of the differential equation.

  3. List of Runge–Kutta methods - Wikipedia

    en.wikipedia.org/wiki/List_of_Runge–Kutta_methods

    The Runge–Kutta–Fehlberg method has two methods of orders 5 and 4; it is sometimes dubbed RKF45 . Its extended Butcher Tableau is: / / / / / / / / / / / / / / / / / / / / / / / / / / The first row of b coefficients gives the fifth-order accurate solution, and the second row has order four.

  4. Standard step method - Wikipedia

    en.wikipedia.org/wiki/Standard_Step_Method

    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 ...

  5. Linear multistep method - Wikipedia

    en.wikipedia.org/wiki/Linear_multistep_method

    Single-step methods (such as Euler's method) refer to only one previous point and its derivative to determine the current value. Methods such as Runge–Kutta take some intermediate steps (for example, a half-step) to obtain a higher order method, but then discard all previous information before taking a second step. Multistep methods attempt ...

  6. Linear function (calculus) - Wikipedia

    en.wikipedia.org/wiki/Linear_function_(calculus)

    The simplest is the slope-intercept form: = +, from which one can immediately see the slope a and the initial value () =, which is the y-intercept of the graph = (). Given a slope a and one known value () =, we write the point-slope form:

  7. Graph of a function - Wikipedia

    en.wikipedia.org/wiki/Graph_of_a_function

    Given a function: from a set X (the domain) to a set Y (the codomain), the graph of the function is the set [4] = {(, ()):}, which is a subset of the Cartesian product.In the definition of a function in terms of set theory, it is common to identify a function with its graph, although, formally, a function is formed by the triple consisting of its domain, its codomain and its graph.

  8. Slope field - Wikipedia

    en.wikipedia.org/wiki/Slope_field

    Solutions to a slope field are functions drawn as solid curves. A slope field shows the slope of a differential equation at certain vertical and horizontal intervals on the x-y plane, and can be used to determine the approximate tangent slope at a point on a curve, where the curve is some solution to the differential equation.

  9. Linear function - Wikipedia

    en.wikipedia.org/wiki/Linear_function

    When the function is of only one variable, it is of the form = +, where a and b are constants, often real numbers. The graph of such a function of one variable is a nonvertical line. a is frequently referred to as the slope of the line, and b as the intercept. If a > 0 then the gradient is positive and the graph slopes upwards.

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