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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 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...
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RADAU
- Referenced in 76 articles
[sw01118]
- RADAU5 implicit Runge-Kutta method of order 5 (Radau IIA) for problems of the form...
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SIMSON
- Referenced in 42 articles
[sw13385]
- performed using a third order Runge-Kutta method for the advective and forcing terms...
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RKC
- Referenced in 120 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...
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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 Runge-Kutta methods are explained, and it is shown...
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MIRKDC
- Referenced in 36 articles
[sw07159]
- Runge-Kutta (MIRK) formulas are implicit Runge-Kutta methods, for which the stages are defined...
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RRK_rr
- Referenced in 16 articles
[sw34461]
- Relaxation Runge-Kutta methods are modifications of Runge-Kutta methods that enforce conservation, dissipation ... relaxation parameter that multiplies the Runge-Kutta update at each time step. Moreover, other desirable ... applied to both explicit and implicit Runge-Kutta methods and requires only a small modification...
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pySDC
- Referenced in 27 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...
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twpbvp
- Referenced in 23 articles
[sw10052]
- correction scheme based on Mono-Implicit Runge-Kutta methods (MIRK...
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hgm R
- Referenced in 21 articles
[sw08770]
- numerical analysis such as the Runge-Kutta method of solving ordinary differential equations and efficient...
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ddesd
- Referenced in 20 articles
[sw35136]
- ordinary differential equations (ODEs) with Runge-Kutta methods that have continuous extensions. For some methods...
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ImplicitLNLMethods
- Referenced in 10 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...
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SERK2
- Referenced in 11 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...
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DESIRE
- Referenced in 12 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...
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GELDA
- Referenced in 33 articles
[sw00331]
- DAEs. In GELDA the BDF methods [1] and Runge-Kutta schemes [6],[7] are implemented...
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Rk-opt
- Referenced in 9 articles
[sw17497]
- 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...
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ABDPACK
- Referenced in 14 articles
[sw01221]
- multiple shooting techniques and implicit Runge-Kutta methods for solving two-point boundary value problems...
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bvptwp.m
- Referenced in 12 articles
[sw10030]
- correction scheme based on Mono-Implicit Runge-Kutta methods (MIRK); the other codes...
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FATODE
- Referenced in 9 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...
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DKLAG6
- Referenced in 11 articles
[sw01068]
- based on continuously imbedded sixth-order Runge-Kutta methods for the solution of state-dependent...