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2. Runge–Kutta–Fehlberg method - Wikipedia

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

   In mathematics, the Runge–Kutta–Fehlberg method (or Fehlberg method) is an algorithm in numerical analysis for the numerical solution of ordinary differential equations. It was developed by the German mathematician Erwin Fehlberg and is based on the large class of Runge–Kutta methods. The novelty of Fehlberg's method is that it is an ...

3. Adomian decomposition method - Wikipedia

   en.wikipedia.org/wiki/Adomian_decomposition_method

   The Adomian decomposition method (ADM) is a semi-analytical method for solving ordinary and partial nonlinear differential equations. The method was developed from the 1970s to the 1990s by George Adomian, chair of the Center for Applied Mathematics at the University of Georgia. [1] It is further extensible to stochastic systems by using the ...

4. Numerical methods for ordinary differential equations

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

   The same illustration for The midpoint method converges faster than the Euler method, as . Numerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to ...

5. Euler method - Wikipedia

   en.wikipedia.org/wiki/Euler_method

   In mathematics and computational science, the Euler method (also called the forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value. It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta ...

6. Rosenbrock methods - Wikipedia

   en.wikipedia.org/wiki/Rosenbrock_methods

   Rosenbrock search is a numerical optimization algorithm applicable to optimization problems in which the objective function is inexpensive to compute and the derivative either does not exist or cannot be computed efficiently. [5] The idea of Rosenbrock search is also used to initialize some root-finding routines, such as fzero (based on Brent's ...

7. Ordinary differential equation - Wikipedia

   en.wikipedia.org/wiki/Ordinary_differential_equation

   e. In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown (s) consists of one (or more) function (s) and involves the derivatives of those functions. [1] The term "ordinary" is used in contrast with partial differential equations ...

8. Exponential integrator - Wikipedia

   en.wikipedia.org/wiki/Exponential_integrator

   Exponential integrators are a class of numerical methods for the solution of ordinary differential equations, specifically initial value problems. This large class of methods from numerical analysis is based on the exact integration of the linear part of the initial value problem. Because the linear part is integrated exactly, this can help to ...

9. Linear multistep method - Wikipedia

   en.wikipedia.org/wiki/Linear_multistep_method

   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.