- Referenced in 75 articles
- RADAU5 implicit Runge-Kutta method of order 5 (Radau IIA) for problems of the form...
- Referenced in 38 articles
- 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...
- Referenced in 108 articles
- 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...
- Referenced in 36 articles
- performed using a third order Runge-Kutta method for the advective and forcing terms...
- Referenced in 35 articles
- Runge-Kutta (MIRK) formulas are implicit Runge-Kutta methods, for which the stages are defined...
- Referenced in 32 articles
- 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...
- Referenced in 25 articles
- 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...
- Referenced in 21 articles
- correction scheme based on Mono-Implicit Runge-Kutta methods (MIRK...
- Referenced in 19 articles
- ordinary differential equations (ODEs) with Runge-Kutta methods that have continuous extensions. For some methods...
- Referenced in 17 articles
- numerical analysis such as the Runge-Kutta method of solving ordinary differential equations and efficient...
- Referenced in 12 articles
- 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...
- Referenced in 33 articles
- DAEs. In GELDA the BDF methods  and Runge-Kutta schemes , are implemented...
- Referenced in 9 articles
- 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...
- Referenced in 13 articles
- multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems...
- Referenced in 6 articles
- 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...
- Referenced in 7 articles
- MATLAB code for designing optimized Runge-Kutta methods. It is primarily developed and used ... packages: RK-coeff-opt: Find optimal Runge-Kutta 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 Runge-Kutta methods. For a much more extensive package...
- Referenced in 11 articles
- based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent...
- Referenced in 10 articles
- boundaries. High-order explicit and implicit Runge-Kutta methods are used for the time integration...
- Referenced in 10 articles
- Forward, tangent linear, and adjoint Runge-Kutta methods in KPP-2.2. This paper presents...
- Referenced in 8 articles
- 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...