Related papers: Multi-rate Runge-Kutta methods: stability analysis…
We study the A-stability and accuracy characteristics of Clenshaw-Curtis collocation. We present closed-form expressions to evaluate the Runge-Kutta coefficients of these methods. From the A-stability study, Clenshaw-Curtis methods are…
Multirate methods have been used for decades to temporally evolve initial-value problems in which different components evolve on distinct time scales, and thus use of different step sizes for these components can result in increased…
Explicit stabilized methods are an efficient alternative to implicit schemes for the time integration of stiff systems of differential equations in large dimension. In this paper, we derive explicit stabilized integrators of orders one and…
Robustness of linear systems with constant coefficients is considered. There exist methods and tools for analyzing the stability of systems with random or deterministic uncertainties. At the same time, there are no approaches for the…
This work introduces a new class of Runge-Kutta methods for solving nonlinearly partitioned initial value problems. These new methods, named nonlinearly partitioned Runge-Kutta (NPRK), generalize existing additive and component-partitioned…
While traditional robotic systems come with a monolithic system design, reconfigurable multi-robot systems can share and shift physical resources in an on-demand fashion. Multi-robot operations can benefit from this flexibility by actively…
It is difficult to design high order numerical schemes which could preserve both the maximum bound property (MBP) and energy dissipation law for certain phase field equations. Strong stability preserving (SSP) Runge-Kutta methods have been…
As supercomputers grow in hardware complexity, their susceptibility to faults increases and measures need to be taken to ensure the correctness of results. Some numerical algorithms have certain characteristics that allow them to recover…
This paper considers master equations for Markovian kinetic schemes that possess the detailed balance property. Chemical kinetics, as a prime example, often yields large-scale, highly stiff equations. Based on chemical intuitions, Sumiya et…
Maintaining safety under adaptation has long been considered to be an important capability for autonomous systems. As these systems estimate and change the ego-model of the system dynamics, questions regarding how to develop safety…
We provide a note on continuous-stage Runge-Kutta methods (csRK) for solving initial value problems of first-order ordinary differential equations. Such methods, as an interesting and creative extension of traditional Runge-Kutta (RK)…
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…
This work presents a new evolutionary optimization algorithm in theoretical mathematics with important applications in scientific computing. The use of the evolutionary algorithm is justified by the difficulty of the study of the…
A unified theoretical framework is suggested to examine the energy dissipation properties at all stages of additive implicit-explicit Runge-Kutta (IERK) methods up to fourth-order accuracy for gradient flow problems. We construct some…
Optimal Strong Stability Preserving (SSP) Runge--Kutta methods has been widely investegated in the last decade and many open conjectures have been formulated. The iterated implicit midpoint rule has been observed numerically optimal in…
The paper presents a new stiffness modelling method for multi-chain parallel robotic manipulators with flexible links and compliant actuating joints. In contrast to other works, the method involves a FEA-based link stiffness evaluation and…
The use of multivalued controls derived from a special maximal monotone operator are studied in this note. Starting with a strictly passive linear system (with possible parametric uncertainty and external disturbances) a multivalued control…
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…
Mixed-precision methods combine low and high precision arithmetics to exploit low precision computational speed and high precision accuracy. Large ODE systems that contain many heterogeneous interactions lead to a high computational cost…
A high-order multi-time-step (MTS) scheme for the bond-based peridynamic (PD) model, an extension of classical continuous mechanics widely used for analyzing discontinuous problems like cracks, is proposed. The MTS scheme discretizes the…