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Ordinary differential equations occur in many scientific disciplines, including physics, chemistry, biology, and economics. [1] In addition, some methods in numerical partial differential equations convert the partial differential equation into an ordinary differential equation, which must then be solved.
In mathematics, a collocation method is a method for the numerical solution of ordinary differential equations, partial differential equations and integral equations.The idea is to choose a finite-dimensional space of candidate solutions (usually polynomials up to a certain degree) and a number of points in the domain (called collocation points), and to select that solution which satisfies the ...
Some solutions of a differential equation having a regular singular point with indicial roots = and .. In mathematics, the method of Frobenius, named after Ferdinand Georg Frobenius, is a way to find an infinite series solution for a linear second-order ordinary differential equation of the form ″ + ′ + = with ′ and ″.
Numerical methods for ordinary differential equations approximate solutions to initial value problems of the form ′ = (,), =.. The result is approximations for the value of () at discrete times : = +, where is the time step (sometimes referred to as ) and is an integer.
In numerical analysis, a branch of applied mathematics, the midpoint method is a one-step method for numerically solving the differential equation, ′ = (, ()), =. The explicit midpoint method is given by the formula
Numerov's method (also called Cowell's method) is a numerical method to solve ordinary differential equations of second order in which the first-order term does not appear. It is a fourth-order linear multistep method. The method is implicit, but can be made explicit if the differential equation is linear.
In numerical analysis, predictor–corrector methods belong to a class of algorithms designed to integrate ordinary differential equations – to find an unknown function that satisfies a given differential equation. All such algorithms proceed in two steps:
In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable.As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. [1]
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