Related papers: Explicit and Effectively Symmetric Runge-Kutta Met…
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…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…
Gamma distributed delay differential equations (DDEs) arise naturally in many modelling applications. However, appropriate numerical methods for generic Gamma distributed DDEs are not currently available. Accordingly, modellers often resort…
We present a novel and general methodology for building second-order finite volume implicit-explicit Runge-Kutta numerical schemes for solving two-dimensional financial parabolic PDEs with mixed derivatives. The methods achieve second-order…
Symplectic integration of autonomous Hamiltonian systems is a well-known field of study in geometric numerical integration, but for non-autonomous systems the situation is less clear, since symplectic structure requires an even number of…
In this paper, we construct stochastic symplectic Runge--Kutta (SSRK) methods of high strong order for Hamiltonian systems with additive noise. By means of colored rooted tree theory, we combine conditions of mean-square order 1.5 and…
The aim of this paper is to construct and analyze explicit exponential Runge-Kutta methods for the temporal discretization of linear and semilinear integro-differential equations. By expanding the errors of the numerical method in terms of…
Statistical regression models whose mean functions are represented by ordinary differential equations (ODEs) can be used to describe phenomenons dynamical in nature, which are abundant in areas such as biology, climatology and genetics. The…
Runge-Kutta methods are a popular class of numerical methods for solving ordinary differential equations. Every Runge-Kutta method is characterized by two basic parameters: its order, which measures the accuracy of the solution it produces,…
Identifying a full basis of operators to a given order is key to the generality of Effective Field Theory (EFT) and is by now a problem of known solution in terms of the Hilbert series. The present work is concerned with hidden symmetry in…
When evolving in time the solution of a hyperbolic partial differential equation, it is often desirable to use high order strong stability preserving (SSP) time discretizations. These time discretizations preserve the monotonicity…
Runge-Kutta (RK) methods may exhibit order reduction when applied to stiff problems. For linear problems with time-independent operators, order reduction can be avoided if the method satisfies certain weak stage order (WSO) conditions,…
Integration of Ordinary Differential Equations (ODEs) using Backward Difference formula (BDF) methods with p backward steps achieves order p accuracy if specific conditions are met. This work extends the composition technique with complex…
There exist many Runge-Kutta methods (explicit or implicit), more or less adapted to specific problems. Some of them have interesting properties, such as stability for stiff problems or symplectic capability for problems with energy…
This article presents a new approach to the real-time solution of inverse problems on embedded systems. The class of problems addressed corresponds to ordinary differential equations (ODEs) with generalized linear constraints, whereby the…
This paper proposes a new second-order symmetric algorithm for solving decoupled forward-backward stochastic differential equations. Inspired by the alternating direction implicit splitting method for partial differential equations, we…
Recent years have seen an increasing amount of research devoted to the development of so-called resonance-based methods for dispersive nonlinear partial differential equations. In many situations, this new class of methods allows for…
Efficient high order numerical methods for evolving the solution of an ordinary differential equation are widely used. The popular Runge--Kutta methods, linear multi-step methods, and more broadly general linear methods, all have a global…
This study develops a novel multiscale computational method for heat conduction problems of composite structures with diverse periodic configurations in different subdomains. Firstly, the second-order two-scale (SOTS) solutions for these…
This paper studies diagonal implicit symplectic extended Runge--Kutta--Nystr\"{o}m (ERKN) methods for solving the oscillatory Hamiltonian system $H(q,p)=\dfrac{1}{2}p^{T}p+\dfrac{1}{2}q^{T}Mq+U(q)$. Based on symplectic conditions and order…