# What are the Wolfram Mathematica NDSolve function methods?

What are the Wolfram Mathematica NDSolve function methods? I know that in Wolfram Mathematica I can specify solving method in NDSolve function, but I can't find a full list of available methods in documentation.

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Note that the NDSolve's documentation page is available on-line. You can find the list of methods by clicking "More Information". – Sasha Nov 17 '11 at 20:35
You could find this and this useful as well! Good luck! ... could someone please correct how my hyperlink code looks like here? I just hate that! – drN Mar 27 '12 at 0:41
better question for mathematica.stackexchange.com – Abhranil Das Apr 13 '15 at 15:19

These are some of the methods:

"Adams" - predictor-corrector Adams method with orders 1 through 12

"BDF" - Gear implicit backward differentiation formulas with orders 1 through 5

"ExplicitRungeKutta" - adaptive embedded pairs of 2(1) through 9(8) Runge-Kutta methods

"ImplicitRungeKutta" - families of arbitrary-order implicit Runge-Kutta methods

"SymplecticPartitionedRungeKutta" - interleaved Runge-Kutta methods for separable Hamiltonian systems

"MethodOfLines" - method of lines for solution of PDEs

"Extrapolation" - (Gragg-)Bulirsch-Stoer extrapolation method, with possible submethods

• "ExplicitEuler" - forward Euler method

• "ExplicitMidpoint" - midpoint rule method

• "ExplicitModifiedMidpoint" - midpoint rule method with Gragg smoothing

• "LinearlyImplicitEuler" - linearly implicit Euler method

• "LinearlyImplicitMidpoint" - linearly implicit midpoint rule method

• "LinearlyImplicitModifiedMidpoint" - linearly implicit Bader-smoothed midpoint rule method

"DoubleStep" - "baby" version of "Extrapolation"

"LocallyExact" - numerical approximation to locally exact symbolic solution

"StiffnessSwitching" - allows switching between nonstiff and stiff methods in the middle of the integration

"Projection" - invariant-preserving method

"OrthogonalProjection" - method that preserves orthonormality of solutions

"IDA" - general purpose solver for the initial value problem for systems of differential-algebraic equations (DAEs)

"Shooting" - shooting method for BVPs

"Chasing" - Gelfand-Lokutsiyevskii chasing method for BVPs

"EventLocator" - event location for detecting discontinuities, periods, etc.

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Big thanks to you. – Philipp G. Sinicyn Nov 17 '11 at 19:53