New Integration Methods for Perturbed ODEs Based on Symplectic Implicit Runge–Kutta Schemes with Application to Solar System Simulations
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DOI: 10.1007/s10915-017-0634-1
Abstract: We propose a family of integrators, flow-composed implicit Runge–Kutta methods, for perturbations of nonlinear ordinary differential equations, consisting of the composition of flows of the unperturbed part alternated with one step of an implicit Runge–Kutta… read more here.
Keywords: solar system; system; implicit runge; runge kutta ... 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
Diagonally Implicit Runge-Kutta Type Method for Directly Solving Special Fourth-Order Ordinary Differential Equations with Ill-Posed Problem of a Beam on Elastic Foundation
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DOI: 10.3390/a12010010
Abstract: In this study, fifth-order and sixth-order diagonally implicit Runge–Kutta type (DIRKT) techniques for solving fourth-order ordinary differential equations (ODEs) are derived which are denoted as DIRKT5 and DIRKT6, respectively. The first method has three and… read more here.
Keywords: diagonally implicit; order; implicit runge; runge kutta ... See more keywords
Development of an Efficient Diagonally Implicit Runge-Kutta-Nyström 5(4) Pair for Special Second Order IVPs
Sign Up to like & getrecommendations! Published in 2022 at "Axioms"
DOI: 10.3390/axioms11100565
Abstract: In this work, a new pair of diagonally implicit Runge–Kutta–Nyström methods with four stages is constructed. The proposed method has been derived to solve initial value problems of special second-order ordinary-differential equations. The principal local… read more here.
Keywords: runge kutta; pair; diagonally implicit; special second ... See more keywords