
RADAU
 Referenced in 75 articles
[sw01118]
 RADAU5 implicit RungeKutta method of order 5 (Radau IIA) for problems of the form...

LIMbook
 Referenced in 44 articles
[sw14520]
 branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution ... basic knowledge of numerical quadrature and RungeKutta methods, this selfcontained book begins with ... introduction to the line integral methods. It describes numerous Hamiltonian problems encountered in a variety ... line integral methods: the energyconserving RungeKutta methods, also known as Hamiltonian boundary value...

RKC
 Referenced in 115 articles
[sw00808]
 solver for parabolic PDEs. An explicit RungeKuttaChebychev algorithm for parabolic partial differential equations ... tested. This method exploits some remarkable properties of a class of RungeKutta formulas ... stage (s≥2) method is discussed and analytical expressions for its coefficients are derived...

SIMSON
 Referenced in 38 articles
[sw13385]
 performed using a third order RungeKutta method for the advective and forcing terms...

RADAR5
 Referenced in 36 articles
[sw08709]
 Implementing Radau IIA methods for stiff delay differential equations. This article discusses the numerical solution ... encounted in the implementation of implicit RungeKutta methods are explained, and it is shown...

MIRKDC
 Referenced in 36 articles
[sw07159]
 RungeKutta (MIRK) formulas are implicit RungeKutta methods, for which the stages are defined...

pySDC
 Referenced in 25 articles
[sw16754]
 slow dynamics are resolved. The method causes little numerical diffusion and its semidiscrete phase speed ... Kutta (DIRK) and implicitexplicit (IMEX) RungeKutta methods and found to be competitive...

twpbvp
 Referenced in 21 articles
[sw10052]
 correction scheme based on MonoImplicit RungeKutta methods (MIRK...

hgm R
 Referenced in 20 articles
[sw08770]
 numerical analysis such as the RungeKutta method of solving ordinary differential equations and efficient...

ddesd
 Referenced in 20 articles
[sw35136]
 ordinary differential equations (ODEs) with RungeKutta methods that have continuous extensions. For some methods...

RRK_rr
 Referenced in 11 articles
[sw34461]
 Relaxation RungeKutta methods are modifications of RungeKutta methods that enforce conservation, dissipation ... relaxation parameter that multiplies the RungeKutta update at each time step. Moreover, other desirable ... applied to both explicit and implicit RungeKutta methods and requires only a small modification...

SERK2
 Referenced in 11 articles
[sw10426]
 secondorder stabilized explicit RungeKutta method for stiff problems. Traditionally, explicit numerical algorithms have ... ODEs with very large dimension. Stabilized RungeKutta methods (also called RungeKuttaChebyshev methods ... avoid these difficulties. The RungeKutta methods are explicit methods with extended stability domains, usually...

DESIRE
 Referenced in 12 articles
[sw09193]
 DESIRE: Diagonally extended singly implicit RungeKutta effective order methods. In the last approximatly ... years many classes of singlyimplicit RungeKutta methods (SIRK) have been developed. More general ... DESI) methods. A generalization in a different direction are the effective SIRK methods (ESIRK ... DESIRE (diagonally extended singlyimplicit RungeKutta effective order methods). The idea is to combine...

ImplicitLNLMethods
 Referenced in 8 articles
[sw23184]
 implicitexplicit strong stability preserving RungeKutta methods with high linear order. Strong stability preserving ... known that implicit SSP RungeKutta methods exist only up to sixth order; however ... find implicit SSP RungeKutta methods of any linear order. In the current work ... find implicit SSP RungeKutta methods with high linear order...

GELDA
 Referenced in 33 articles
[sw00331]
 DAEs. In GELDA the BDF methods [1] and RungeKutta schemes [6],[7] are implemented...

ABDPACK
 Referenced in 14 articles
[sw01221]
 multiple shooting techniques and implicit RungeKutta methods for solving twopoint boundary value problems...

Rkopt
 Referenced in 8 articles
[sw17497]
 MATLAB code for designing optimized RungeKutta methods. It is primarily developed and used ... packages: RKcoeffopt: Find optimal RungeKutta method coefficients, for a prescribed order ... Includes capabilities for both multistep and multistage methods. polyopt: Find optimal stability polynomials ... analyzing or computing various properties of RungeKutta methods. For a much more extensive package...

DKLAG6
 Referenced in 11 articles
[sw01068]
 based on continuously imbedded sixthorder RungeKutta methods for the solution of statedependent...

Aghora
 Referenced in 10 articles
[sw13971]
 boundaries. Highorder explicit and implicit RungeKutta methods are used for the time integration...

KPP
 Referenced in 10 articles
[sw10179]
 Forward, tangent linear, and adjoint RungeKutta methods in KPP2.2. This paper presents...