相关论文: Exponentially fitted methods that preserve conserv…

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions.…

Unitary transformations are an essential tool for the theoretical understanding of many systems by mapping them to simpler effective models. A systematically controlled variant to perform such a mapping is a perturbative continuous unitary…

We address the problem of constructing approximations based on orthogonal polynomials that preserve an arbitrary set of moments of a given function without loosing the spectral convergence property. To this aim, we compute the constrained…

In the paper explicit functional continuous Runge-Kutta and Runge-Kutta-Nystr\"om methods for retarded functional differential equations are considered. New methods for first order equations as well as for second order equations of the…

We prove that Runge-Kutta (RK) methods for numerical integration of arbitrarily large systems of Ordinary Differential Equations are linearly stable. Standard stability arguments -- based on spectral analysis, resolvent condition or strong…

In this work, we present a positivity-preserving entropy-based adaptive filtering method for shock capturing in discontinuous spectral element methods. By adapting the filter strength to enforce positivity and a local discrete minimum…

Structure-preserving algorithms for solving conservative PDEs with added linear dissipation are generalized to systems with time-dependent damping/driving terms. This study is motivated by several PDE models of physical phenomena, such as…

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…

We prove the exponential convergence to the equilibrium, quantified by R\'enyi divergence, of the solution of the Fokker-Planck equation with drift given by the gradient of a strictly convex potential. This extends the classical exponential…

Finite volume methods are proposed for computing approximate pathwise entropy/kinetic solutions to conservation laws with a rough path dependent flux function. For a convex flux, it is demonstrated that rough path oscillations may lead to…

We present a C++ implementation of a fifth order semi-implicit Runge-Kutta algorithm for solving Ordinary Differential Equations. This algorithm can be used for studying many different problems and in particular it can be applied for…

A new approach to the construction of difference schemes of any order for the many-body problem that preserves all its algebraic integrals is proposed. We introduced additional variables, namely, distances and reciprocal distances between…

The properties of the Bigeometric or proportional derivative are presented and discussed explicitly. Based on this derivative, the Bigeometric Taylor theorem is worked out. As an application of this calculus, the Bigeometric Runge-Kutta…

In this paper, the nonlinear Rosenau-Hyman equation with time dependent variable coefficients is considered for investigating its invariant properties, exact solutions and conservation laws. Using Lie classical method, we derive symmetries…

Solving large-scale eigenvalue problems poses a significant challenge due to the computational complexity and limitations on the parallel scalability of the orthogonalization operation, when many eigenpairs are required. In this paper, we…

Radiation hydrodynamics simulations based on the one-fluid two-temperature model may violate the law of energy conservation because the governing equations are expressed in a nonconservative formulation. Here, we maintain the important…

This work constructs the first-ever sixth-order exponential Runge--Kutta (ExpRK) methods for the time integration of stiff parabolic PDEs. First, we leverage the exponential B-series theory to restate the stiff order conditions for ExpRK…

Energy preserving numerical methods for a certain class of PDEs are derived, applying the partition of unity method. The methods are extended to also be applicable in combination with moving mesh methods by the rezoning approach. These…

Many applications involve partial differential equations which admits nontrivial steady state solutions. The design of schemes which are able to describe correctly these equilibrium states may be challenging for numerical methods, in…

A new method named rational expansion method of exponent function is presented to find exact traveling wave solutions of differential-difference equations. This method generalizes the so-called tanh-method and other similar methods. Some…