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Predictor–corrector methods for solving ODEs [ edit ] When considering the numerical solution of ordinary differential equations (ODEs) , a predictor–corrector method typically uses an explicit method for the predictor step and an implicit method for the corrector step.
In numerical analysis, the Dormand–Prince (RKDP) method or DOPRI method, is an embedded method for solving ordinary differential equations (ODE). [1] The method is a member of the Runge–Kutta family of ODE solvers. More specifically, it uses six function evaluations to calculate fourth- and fifth-order accurate solutions.
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.
Method of lines - the example, which shows the origin of the name of method. The method of lines (MOL, NMOL, NUMOL [1] [2] [3]) is a technique for solving partial differential equations (PDEs) in which all but one dimension is discretized.
It is the most basic explicit method for numerical integration of ordinary differential equations and is the simplest Runge–Kutta method. The Euler method is named after Leonhard Euler , who first proposed it in his book Institutionum calculi integralis (published 1768–1770).
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 ...
Spectral methods can be used to solve differential equations (PDEs, ODEs, eigenvalue, etc) and optimization problems. When applying spectral methods to time-dependent PDEs, the solution is typically written as a sum of basis functions with time-dependent coefficients; substituting this in the PDE yields a system of ODEs in the coefficients ...
Butcher, John C. (2003), Numerical Methods for Ordinary Differential Equations, John Wiley, ISBN 978-0-471-96758-3. Dahlquist, Germund (1956), "Convergence and stability in the numerical integration of ordinary differential equations", Mathematica Scandinavica, 4: 33– 53, doi: 10.7146/math.scand.a-10454.