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  2. Bogacki–Shampine method - Wikipedia

    en.wikipedia.org/wiki/Bogacki–Shampine_method

    The Bogacki–Shampine method is implemented in the ode3 for fixed step solver and ode23 for a variable step solver function in MATLAB (Shampine & Reichelt 1997). Low-order methods are more suitable than higher-order methods like the Dormand–Prince method of order five, if only a crude approximation to the solution is required.

  3. McCabe–Thiele method - Wikipedia

    en.wikipedia.org/wiki/McCabe–Thiele_method

    The rectifying section operating line for the section above the inlet feed stream of the distillation column (shown in green in Figure 1) starts at the intersection of the distillate composition line and the x = y line and continues at a downward slope of L / (D + L), where L is the molar flow rate of reflux and D is the molar flow rate of the ...

  4. Muller's method - Wikipedia

    en.wikipedia.org/wiki/Muller's_method

    Muller's method is a root-finding algorithm, a numerical method for solving equations of the form f(x) = 0.It was first presented by David E. Muller in 1956.. Muller's method proceeds according to a third-order recurrence relation similar to the second-order recurrence relation of the secant method.

  5. Linear multistep method - Wikipedia

    en.wikipedia.org/wiki/Linear_multistep_method

    Linear multistep methods are used for the numerical solution of ordinary differential equations. Conceptually, a numerical method starts from an initial point and then takes a short step forward in time to find the next solution point. The process continues with subsequent steps to map out the solution.

  6. Numerical methods for ordinary differential equations

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

    For example, the second-order equation y′′ = −y can be rewritten as two first-order equations: y′ = z and z′ = −y. In this section, we describe numerical methods for IVPs, and remark that boundary value problems (BVPs) require a different set of tools. In a BVP, one defines values, or components of the solution y at more than one ...

  7. Brent's method - Wikipedia

    en.wikipedia.org/wiki/Brent's_method

    Suppose that we want to solve the equation f(x) = 0. As with the bisection method, we need to initialize Dekker's method with two points, say a 0 and b 0, such that f(a 0) and f(b 0) have opposite signs. If f is continuous on [a 0, b 0], the intermediate value theorem guarantees the existence of a solution between a 0 and b 0.

  8. MUSCL scheme - Wikipedia

    en.wikipedia.org/wiki/MUSCL_scheme

    The diagram opposite shows a 3rd order solution to G A Sod's shock tube problem (Sod, 1978) using the above high resolution Kurganov and Tadmor Central Scheme (KT) but with parabolic reconstruction and van Albada limiter. This again illustrates the effectiveness of the MUSCL approach to solving the Euler equations.

  9. Runge–Kutta–Fehlberg method - Wikipedia

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

    "New high-order Runge-Kutta formulas with step size control for systems of first and second-order differential equations". Zeitschrift für Angewandte Mathematik und Mechanik . 44 (S1): T17 – T29 .