Related papers: Multirate Runge-Kutta for Nonlinearly Partitioned …
Mixed-precision algorithms combine low- and high-precision computations in order to benefit from the performance gains of reduced-precision without sacrificing accuracy. In this work, we design mixed-precision Runge-Kutta-Chebyshev (RKC)…
A general purpose, modular program package for the integration of large number of independent ordinary differential equation systems capable of using professional graphics cards is presented. The available numerical schemes are the explicit…
We present an implementation of a fully stage-parallel preconditioner for Radau IIA type fully implicit Runge--Kutta methods, which approximates the inverse of $A_Q$ from the Butcher tableau by the lower triangular matrix resulting from an…
In this paper we propose a numerical scheme for partitioned systems of index 2 DAEs, such as those arising from nonholonomic mechanical problems and prove the order of a certain class of Runge-Kutta methods we call of Lobatto-type. The…
Modified Patankar-Runge-Kutta (MPRK) methods preserve the positivity as well as conservativity of a production-destruction system (PDS) of ordinary differential equations for all time step sizes. As a result, higher order MPRK schemes do…
Explicit stabilized methods are highly efficient time integrators for large and stiff systems of ordinary differential equations especially when applied to semi-discrete parabolic problems. However, when local spatial mesh refinement is…
We study symplectic numerical integration of mechanical systems with a Hamiltonian specified in non-canonical coordinates and its application to guiding-center motion of charged plasma particles in magnetic confinement devices. The…
In the paper explicit functional continuous Runge-Kutta and Runge-Kutta-Nystr\"om methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the…
A fourth-order, L-stable, exponential time differencing Runge-Kutta type scheme is developed to solve nonlinear systems of reaction diffusion equations with nonsmooth data. The new scheme, ETDRK4RDP, is constructed by approximating the…
Numerous applications necessitate the computation of numerical solutions to differential equations across a wide range of initial conditions and system parameters, which feeds the demand for efficient yet accurate numerical integration…
We introduce a new class of Runge-Kutta type methods suitable for time stepping to propagate hyperbolic solutions within tent-shaped spacetime regions. Unlike standard Runge-Kutta methods, the new methods yield expected convergence…
We propose MRU (Multi-Range Reasoning Units), a new fast compositional encoder for machine comprehension (MC). Our proposed MRU encoders are characterized by multi-ranged gating, executing a series of parameterized contract-and-expand…
This paper develops a new class of linearly implicit time integration schemes called Linearly-Implicit Runge-Kutta-W (LIRK-W) methods. These schemes are based on an implicit-explicit approach which does not require a splitting of the right…
Singly-TASE operators for the numerical solution of stiff differential equations were proposed by Calvo et al. in J.Sci. Comput. 2023 to reduce the computational cost of Runge-Kutta-TASE (RKTASE) methods when the involved linear systems are…
Standard gradient-based iteration algorithms for optimization, such as gradient descent and its various proximal-based extensions to nonsmooth problems, are known to converge slowly for ill-conditioned problems, sometimes requiring many…
In a previous paper, a technique was suggested to avoid order reduction with any explicit exponential Runge-Kutta method when integrating initial boundary value nonlinear problems with time-dependent boundary conditions. In this paper, we…
A framework is presented to design multirate time stepping algorithms for two dissipative models with coupling across a physical interface. The coupling takes the form of boundary conditions imposed on the interface, relating the solution…
The existing discrete variational derivative method is only second-order accurate and fully implicit. In this paper, we propose a framework to construct an arbitrary high-order implicit (original) energy stable scheme and a second-order…
For Hamiltonian systems with non-canonical structure matrices, a new family of fourth-order energy-preserving integrators is presented. The integrators take a form of a combination of Runge--Kutta methods and continuous-stage Runge--Kutta…
High order spatial discretizations with monotonicity properties are often desirable for the solution of hyperbolic PDEs. These methods can advantageously be coupled with high order strong stability preserving time discretizations. The…