Efficient exponential Runge–Kutta methods of high order: construction and implementation
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DOI: 10.1007/s10543-020-00834-z
Abstract: Exponential Runge–Kutta methods have shown to be competitive for the time integration of stiff semilinear parabolic PDEs. The current construction of stiffly accurate exponential Runge–Kutta methods, however, relies on a convergence result that requires weakening… read more here.
Keywords: kutta methods; order; exponential runge; runge kutta ... See more keywords
Delay-dependent stability of symmetric Runge–Kutta methods for second order delay differential equations with three parameters
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DOI: 10.1016/j.apnum.2017.03.005
Abstract: Abstract The paper is concerned with the delay-dependent stability analysis of symmetric Runge–Kutta methods, which include the Gauss methods and the Lobatto IIIA, IIIB and IIIS methods, for the second order delay differential equations with… read more here.
Keywords: symmetric runge; stability; kutta methods; runge kutta ... See more keywords
Stochastic multi-symplectic Runge–Kutta methods for stochastic Hamiltonian PDEs
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DOI: 10.1016/j.apnum.2018.09.011
Abstract: In this paper, we consider stochastic Runge-Kutta methods for stochastic Hamiltonian partial differential equations and present some sufficient conditions for multisymplecticity of stochastic Runge-Kutta methods of stochastic Hamiltonian partial differential equations. Particularly, we apply these… read more here.
Keywords: runge kutta; methods stochastic; kutta methods; multi symplectic ... See more keywords
Variational formulations for explicit Runge-Kutta Methods
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DOI: 10.1016/j.finel.2019.06.007
Abstract: Variational space-time formulations for Partial Differential Equations have been of great interest in the last decades. While it is known that implicit time marching schemes have variational structure, the Galerkin formulation of explicit methods in… read more here.
Keywords: runge kutta; time; explicit runge; kutta methods ... See more keywords
Large Time Step and DC Stable TD-EFIE Discretized With Implicit Runge–Kutta Methods
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DOI: 10.1109/tap.2019.2943443
Abstract: The time domain-electric field integral equation (TD-EFIE) and its differentiated version are widely used to simulate the transient scattering of a time dependent electromagnetic field by a perfect electric conductor (PEC). The time discretization of… read more here.
Keywords: runge kutta; time; kutta methods; time step ... See more keywords
Round-Off Error and Exceptional Behavior Analysis of Explicit Runge-Kutta Methods
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DOI: 10.1109/tc.2019.2917902
Abstract: Numerical integration schemes are mandatory to understand complex behaviors of dynamical systems described by ordinary differential equations. Implementation of these numerical methods involve floating-point computations and propagation of round-off errors. This paper presents a new… read more here.
Keywords: runge kutta; kutta methods; runge; round error ... See more keywords
Oscillation of Runge-Kutta methods for advanced impulsive differential equations with piecewise constant arguments
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DOI: 10.1186/s13662-016-1067-0
Abstract: The purpose of this paper is to study oscillation of Runge-Kutta methods for linear advanced impulsive differential equations with piecewise constant arguments. We obtain conditions of oscillation and nonoscillation for Runge-Kutta methods. Moreover, we prove… read more here.
Keywords: advanced impulsive; kutta methods; runge kutta; oscillation runge ... See more keywords
High Order Two-Derivative Runge-Kutta Methods with Optimized Dispersion and Dissipation Error
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DOI: 10.3390/math9030232
Abstract: In this work we consider explicit Two-derivative Runge-Kutta methods of a specific type where the function f is evaluated only once at each step. New 7th order methods are presented with minimized dispersion and dissipation… read more here.
Keywords: runge kutta; derivative runge; kutta methods; order ... See more keywords