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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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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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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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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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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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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...