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A new algorithm for numerical integration of the rigid-body equations of motion is proposed. The algorithm uses the leapfrog scheme and the quantities involved are angular velocities and orientational variables which can be expressed in…
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,…
We consider a linear inhomogeneous fractional evolution equation which is obtained from a Cauchy problem by replacing its first-order time derivative with Caputo's fractional derivative. The operator in the fractional evolution equation is…
This work focuses on the numerical study of a recently published class of Runge-Kutta methods designed for mixed-precision arithmetic. We employ the methods in solving partial differential equations on modern hardware. In particular we…
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…
In this paper we consider an approach to improve the performance of exponential Runge--Kutta integrators and Lawson schemes} in cases where the solution of a related, but usually much simpler, problem can be computed efficiently. While for…
This work proposes an efficient treatment of continuous-time optimal control problem (OCP) with long horizons and nonlinear least-squares costs. The Gauss-Newton Runge-Kutta (GNRK) integrator is presented which provides a high-order cost…
Mixed precision Runge--Kutta methods have been recently developed and used for the time-evolution of partial differential equations. Two-derivative Runge--Kutta schemes may offer enhanced stability and accuracy properties compared to…
A transient magneto-quasistatic vector potential formulation involving nonlinear material is spatially discretized using the finite element method of first and second polynomial order. By applying a generalized Schur complement the…
The aim of this paper is to construct and analyze exponential Runge-Kutta methods for the temporal discretization of a class of semilinear parabolic problems with arbitrary state-dependent delay. First, the well-posedness of the problem is…
We present a robust and accurate numerical method to solve the modified Buckley-Leverett equation in two-phase porous media flow with dynamic capillary pressure effect. A symmetric interior penalty discontinuous Galerkin method is used to…
We present the implementation of two-moment based general-relativistic multi-group radiation transport module in the $\texttt{G}$eneral-relativistic $\texttt{mu}$ltigrid $\texttt{nu}$merical ($\texttt{Gmunu}$) code. On top of solving the…
In the present paper, a class of stochastic Runge-Kutta methods containing the second order stochastic Runge-Kutta scheme due to E. Platen for the weak approximation of It\^o stochastic differential equation systems with a multi-dimensional…
An 11-dimensional family of embedded (4, 5) pairs of explicit 9-stage Runge-Kutta methods with an interpolant of order 5 is derived. Two optimized for efficiency pairs are presented.
A new approach for the construction of high order A-stable explicit integrators for ordinary differential equations (ODEs) is theoretically studied. Basically, the integrators are obtained by splitting, at each time step, the solution of…
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…
We propose a new probabilistic scheme which combines deep learning techniques with high order schemes for backward stochastic differential equations belonging to the class of Runge-Kutta methods to solve high-dimensional semi-linear…
This paper proposes a numerical method based on the Adomian decomposition approach for the time discretization, applied to Euler equations. A recursive property is demonstrated that allows to formulate the method in an appropriate and…
This report is concerned with the efficiency of numerical methods for simulating quantum spin systems, with the aim to implement an improved method for simulation of a time-dependent Hamiltonian that displays chirped pulses at a high…
While the vast majority of calculations reported on molecular conductance have been based on the static non-equilibrium Green's function formalism combined with density functional theory, in recent years a few time-depedent approaches to…