Related papers: Optimising 4th-Order Runge-Kutta Methods: A Dynami…

In this paper we discuss the use of implicit Runge-Kutta schemes for the time discretization of optimal control problems with evolution equations. The specialty of the considered discretizations is that the discretizations schemes for the…

Explicit Runge-Kutta (RK) integration of hyperbolic initial-boundary value problems with time-dependent Dirichlet data often displays order reduction: the observed convergence order falls below the nominal order because the stage structure…

The recently-introduced relaxation approach for Runge-Kutta methods can be used to enforce conservation of energy in the integration of Hamiltonian systems. We study the behavior of implicit and explicit relaxation Runge-Kutta methods in…

Sampling-based motion planning has emerged as a powerful approach for robotics, enabling exploration of complex, high-dimensional configuration spaces. When combined with Signal Temporal Logic (STL), a temporal logic widely used for…

Classical and new numerical schemes are generated using evolutionary computing. Differential Evolution is used to find the coefficients of finite difference approximations of function derivatives, and of single and multi-step integration…

Constructing explicit Runge--Kutta (ERK) methods with as few stages as possible for a given order is a classical problem in numerical analysis. In this work, we introduce a $Q$/$D$-space framework of sufficient order conditions for ERK…

In this work, we introduce high-order Basis-Update & Galerkin (BUG) integrators based on explicit Runge-Kutta methods for large-scale matrix differential equations. These dynamical low-rank integrators extend the BUG integrator to arbitrary…

We analyze the stability and accuracy (up to third order) of a new family of implicit-explicit Runge-Kutta (IMEX RK) methods. This analysis expedites development of methods with various balances in the number of explicit stages and implicit…

In this paper, we propose a framework based on the Retrospective Approximation (RA) paradigm to solve optimization problems with a stochastic objective function and general nonlinear deterministic constraints. This framework sequentially…

We propose entropy-preserving and entropy-stable partitioned Runge--Kutta (RK) methods. In particular, we extend the explicit relaxation Runge--Kutta methods to IMEX--RK methods and a class of explicit second-order multirate methods for…

Retrieval-Augmented Generation (RAG) has emerged as a widely adopted approach for knowledge injection during large language model (LLM) inference in recent years. However, due to their limited ability to exploit fine-grained inter-document…

Nonlinear parabolic equations are central to numerous applications in science and engineering, posing significant challenges for analytical solutions and necessitating efficient numerical methods. Exponential integrators have recently…

Optimal path planning involves finding a feasible state sequence between a start and a goal that optimizes an objective. This process relies on heuristic functions to guide the search direction. While a robust function can improve search…

In this paper, exponential Runge-Kutta methods of collocation type (ERKC) which were originally proposed in (Appl Numer Math 53:323-339, 2005) are extended to semilinear parabolic problems with time-dependent delay. Two classes of the ERKC…

We present a dynamically load-balanced parallel $ p $-adaptive implicit high-order flux reconstruction method for under-resolved turbulence simulation. The high-order explicit first stage, singly diagonal implicit Runge-Kutta (ESDIRK)…

Explicit Runge-Kutta methods are classical and widespread techniques in the numerical solution of ordinary differential equations (ODEs). Considering partial differential equations, spatial semidiscretisations can be used to obtain systems…

A wide range of physical phenomena exhibit auxiliary admissibility criteria, such as conservation of entropy or various energies, which arise implicitly under exact solution of their governing PDEs. However, standard temporal schemes, such…

We propose an Eulerian-Lagrangian (EL) Runge-Kutta (RK) discontinuous Galerkin (DG) method for wave equations. The method is designed based on the ELDG method for transport problems [J. Comput. Phy. 446: 110632, 2021.], which tracks…

In this paper, authors successfully construct a new algorithm for the new higher order scheme of weak approximation of SDEs. The algorithm presented here is based on [1][2]. Although this algorithm shares some features with the algorithm…

The optimal placement of sensors for environmental monitoring and disaster management is a challenging problem due to its NP-hard nature. Traditional methods for sensor placement involve exact, approximation, or heuristic approaches, with…