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A Friendly Introduction to Numerical Analysis. Upper Saddle River, New Jersey: Pearson Prentice Hall. ISBN 978-0-13-013054-9. J. C. Butcher, Numerical methods for ordinary differential equations, ISBN 0-471-96758-0
Gauss–Legendre methods are implicit Runge–Kutta methods. More specifically, they are collocation methods based on the points of Gauss–Legendre quadrature. The Gauss–Legendre method based on s points has order 2s. [1] All Gauss–Legendre methods are A-stable. [2] The Gauss–Legendre method of order two is the implicit midpoint rule.
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 .
Diagonally Implicit Runge–Kutta (DIRK) formulae have been widely used for the numerical solution of stiff initial value problems; [5] the advantage of this approach is that here the solution may be found sequentially as opposed to simultaneously. The simplest method from this class is the order 2 implicit midpoint method.
Numerical methods for ordinary differential equations, methods used to find numerical approximations to the solutions of ordinary differential equations; Numerical methods for partial differential equations, the branch of numerical analysis that studies the numerical solution of partial differential equations
Download as PDF; Printable version; ... 6th Edition 2012 (later editions with A. D. Snider) ... Computational Methods and Function Theory, Lecture Notes in ...
Adaptive Simpson's method; Boole's rule — sixth-order method, based on the values at five equidistant points; Newton–Cotes formulas — generalizes the above methods; Romberg's method — Richardson extrapolation applied to trapezium rule; Gaussian quadrature — highest possible degree with given number of points
The backward differentiation formula (BDF) is a family of implicit methods for the numerical integration of ordinary differential equations.They are linear multistep methods that, for a given function and time, approximate the derivative of that function using information from already computed time points, thereby increasing the accuracy of the approximation.