Related papers: High order symplectic integrators based on continu…
We perform a classification of third order integrable systems of evolution equations with respect to higher symmetries. Applying it, we consider polynomial systems that are 0-homogeneous under a suitable weighting of variables with main…
In this paper we generalize the polynomial time integration framework to additively partitioned initial value problems. The framework we present is general and enables the construction of many new families of additive integrators with…
Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this…
In this paper, high-order numerical integrators on homogeneous spaces will be presented as an application of nonholonomic partitioned Runge-Kutta Munthe-Kaas (RKMK) methods on Lie groups. A homogeneous space $M$ is a manifold where a group…
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…
In this work, we develop a class of up to third-order energy-stable schemes for the Cahn--Hilliard equation. Building on Lawson's integrating factor Runge--Kutta method, which is widely used for stiff semilinear equations, we discuss its…
We introduce a novel numerical method to integrate partial differential equations representing the Hamiltonian dynamics of field theories. It is a multi-symplectic integrator that locally conserves the stress-energy tensor with an excellent…
The usual explicit finite-difference method of solving partial differential equations is limited in stability because it approximates the exact amplification factor by power-series. By adapting the same exponential-splitting method of…
In this work, we show high order splitting methods of integration without negative steps, allowing us to solve numerically irreversible problems, like reaction-diffusion equations. The methods consist in a suitable affine combinations of…
A novel optimization procedure for the generation of stability polynomials of stabilized explicit Runge-Kutta methods is devised. Intended for semidiscretizations of hyperbolic partial differential equations, the herein developed approach…
A semiclassical formula for the coherent-state propagator requires the determination of specific classical paths inhabiting a complex phase-space through a Hamiltonian flux. Such trajectories are constrained to special boundary conditions…
This work proposes and analyzes a new class of numerical integrators for computing low-rank approximations to solutions of matrix differential equation. We combine an explicit Runge-Kutta method with repeated randomized low-rank…
In this paper, two new families of fourth-order explicit exponential Runge--Kutta (ERK) methods with four stages are studied for solving first-order differential systems $y'(t)+My(t)=f(y(t))$. By comparing the Taylor series of the exact…
In the last few decades, numerical simulation for nonlinear oscillators has received a great deal of attention, and many researchers have been concerned with the design and analysis of numerical methods for solving oscillatory problems. In…
We design a novel, exactly energy-conserving implicit non-symplectic integration method for an eight-dimensional Hamiltonian system with four degrees of freedom. In our algorithm, each partial derivative of the Hamiltonian with respect to…
This paper had no abstract originally. A second-order symplectic integration algorithm for guiding center motion is presented. The algorithm is based on the Poincar\'e (mid-point) generating function.
In previous papers, explicit symplectic integrators were designed for nonrotating black holes, such as a Schwarzschild black hole. However, they fail to work in the Kerr spacetime because not all variables can be separable, or not all…
This paper proposes a higher-order multiscale computational method for nonlinear thermo-electric coupling problems of composite structures, which possess temperature-dependent material properties and nonlinear Joule heating. The innovative…
In this paper, we propose Galerkin-Legendre spectral method with implicit Runge-Kutta method for solving the unsteady two-dimensional Schrodinger equation with nonhomogeneous Dirichlet boundary conditions and initial condition. We apply a…
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…