
LIMbook
 Referenced in 54 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...

RADAU
 Referenced in 76 articles
[sw01118]
 RADAU5 implicit RungeKutta method of order 5 (Radau IIA) for problems of the form...

SIMSON
 Referenced in 42 articles
[sw13385]
 performed using a third order RungeKutta method for the advective and forcing terms...

RKC
 Referenced in 120 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...

RADAR5
 Referenced in 38 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...

RRK_rr
 Referenced in 16 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...

pySDC
 Referenced in 27 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 23 articles
[sw10052]
 correction scheme based on MonoImplicit RungeKutta methods (MIRK...

hgm R
 Referenced in 21 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...

ImplicitLNLMethods
 Referenced in 10 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...

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...

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

Rkopt
 Referenced in 9 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...

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

bvptwp.m
 Referenced in 12 articles
[sw10030]
 correction scheme based on MonoImplicit RungeKutta methods (MIRK); the other codes...

FATODE
 Referenced in 9 articles
[sw11044]
 Fatode implements four families of methods: explicit RungeKutta for nonstiff problems, fully implicit Runge ... implicit RungeKutta, and Rosenbrock for stiff problems. Each family contains several methods with different ... orders of accuracy; users can add new methods by simply providing their coefficients. For each ... analysis capabilities in the context of RungeKutta methods. A wide range of applications...

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