• RADAU

• Referenced in 70 articles [sw01118]
• RADAU5 implicit Runge-Kutta method of order 5 (Radau IIA) for problems of the form...

• MIRKDC

• Referenced in 34 articles [sw07159]
• Runge-Kutta (MIRK) formulas are implicit Runge-Kutta methods, for which the stages are defined...

• RKC

• Referenced in 95 articles [sw00808]
• solver for parabolic PDEs. An explicit Runge-Kutta-Chebychev algorithm for parabolic partial differential equations ... tested. This method exploits some remarkable properties of a class of Runge-Kutta formulas ... stage (s≥2) method is discussed and analytical expressions for its coefficients are derived...

• RADAR5

• Referenced in 30 articles [sw08709]
• Implementing Radau IIA methods for stiff delay differential equations. This article discusses the numerical solution ... encounted in the implementation of implicit Runge-Kutta methods are explained, and it is shown...

• SIMSON

• Referenced in 28 articles [sw13385]
• performed using a third order Runge-Kutta method for the advective and forcing terms...

• twpbvp

• Referenced in 19 articles [sw10052]
• correction scheme based on Mono-Implicit Runge-Kutta methods (MIRK...

• DESIRE

• Referenced in 11 articles [sw09193]
• DESIRE: Diagonally extended singly implicit Runge-Kutta effective order methods. In the last approximatly ... years many classes of singly-implicit Runge-Kutta methods (SIRK) have been developed. More general ... DESI) methods. A generalization in a different direction are the effective SIRK methods (ESIRK ... DESIRE (diagonally extended singly-implicit Runge-Kutta effective order methods). The idea is to combine...

• GELDA

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

• LIMbook

• Referenced in 9 articles [sw14520]
• branch of numerical analysis that devises numerical methods able to reproduce (in the discrete solution ... basic knowledge of numerical quadrature and Runge-Kutta methods, this self-contained book begins with ... introduction to the line integral methods. It describes numerous Hamiltonian problems encountered in a variety ... line integral methods: the energy-conserving Runge-Kutta methods, also known as Hamiltonian boundary value...

• pySDC

• Referenced in 13 articles [sw16754]
• slow dynamics are resolved. The method causes little numerical diffusion and its semidiscrete phase speed ... Kutta (DIRK) and implicit-explicit (IMEX) Runge-Kutta methods and found to be competitive...

• hgm R

• Referenced in 12 articles [sw08770]
• numerical analysis such as the Runge-Kutta method of solving ordinary differential equations and efficient...

• SERK2

• Referenced in 7 articles [sw10426]
• second-order stabilized explicit Runge-Kutta method for stiff problems. Traditionally, explicit numerical algorithms have ... ODEs with very large dimension. Stabilized Runge-Kutta methods (also called Runge-Kutta-Chebyshev methods ... avoid these difficulties. The Runge-Kutta methods are explicit methods with extended stability domains, usually...

• ABDPACK

• Referenced in 12 articles [sw01221]
• multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems...

• DKLAG6

• Referenced in 11 articles [sw01068]
• based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent...

• KPP

• Referenced in 10 articles [sw10179]
• Forward, tangent linear, and adjoint Runge-Kutta methods in KPP-2.2. This paper presents...

• GniCodes

• Referenced in 8 articles [sw21086]
• integrators, (partitioned) Runge-Kutta methods, composition and splitting methods, linear multistep methods, and algorithms ... Matlab codes for implicit Runge-Kutta, composition, and multistep methods. The final Section 5 gives...

• WENOCLAW

• Referenced in 8 articles [sw07611]
• notions of wave propagation and the method of lines, and can in principle be extended ... solver. In this work, we use Runge-Kutta methods...

• S-ROCK

• Referenced in 30 articles [sw11792]
• equations (SDEs). These methods, called S-ROCK (for stochastic orthogonal Runge-Kutta Chebyshev), are explicit ... much more efficient than the standard explicit methods proposed so far for stochastic problems...

• FATODE

• Referenced in 5 articles [sw11044]
• Fatode implements four families of methods: explicit Runge-Kutta for nonstiff problems, fully implicit Runge ... implicit Runge-Kutta, 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 Runge-Kutta methods. A wide range of applications...

• ImplicitLNLMethods

• Referenced in 3 articles [sw23184]
• implicit-explicit strong stability preserving Runge-Kutta methods with high linear order. Strong stability preserving ... known that implicit SSP Runge-Kutta methods exist only up to sixth order; however ... find implicit SSP Runge-Kutta methods of any linear order. In the current work ... find implicit SSP Runge-Kutta methods with high linear order...