Related papers: Exponential Fourier collocation methods for solvin…
In this paper, we propose and analyse a novel class of exponential collocation methods for solving conservative or dissipative systems based on exponential integrators and collocation methods. It is shown that these novel methods can be of…
A novel efficient and high accuracy numerical method for the time-fractional differential equations (TFDEs) is proposed in this work. We show the equivalence between TFDEs and the integer-order extended parametric differential equations…
In this paper, a class of high-order methods to numerically solve Functional Differential Equations with Piecewise Continuous Arguments (FDEPCAs) is discussed. The framework stems from the expansion of the vector field associated with the…
In the present work, a kind of trigonometric collocation methods based on Lagrange basis polynomials is developed for effectively solving multi-frequency oscillatory second-order differential equations…
In this paper we extend the polynomial time integration framework to include exponential integration for both partitioned and unpartitioned initial value problems. We then demonstrate the utility of the exponential polynomial framework by…
High-dimensional Partial Differential Equations (PDEs) are a popular mathematical modelling tool, with applications ranging from finance to computational chemistry. However, standard numerical techniques for solving these PDEs are typically…
Multiphysics problems involving two or more coupled physical phenomena are ubiquitous in science and engineering. This work develops a new partitioned exponential approach for the time integration of multiphysics problems. After a possible…
In this paper, we obtain results on exponential stability of second order delay differential equations, which are based on a version of the Floquet theory for delay differential equations of the second order we proposed. Our version allows…
We present direct logarithmically optimal in theory and fast in practice algorithms to implement the tensor product high order finite element method on multi-dimensional rectangular parallelepipeds for solving PDEs of the Poisson kind. They…
In this paper we discuss the efficient implementation of RKN-type Fourier collocation methods, which are used when solving second-order differential equations. The proposed implementation relies on an alternative formulation of the methods…
Recent developments in high peak-power table-top laser systems reaching highly relativistic light intensities have led to significant advances in laser-driven particle acceleration schemes (mainly the laser wakefield acceleration, LWFA)…
We propose high-order FDTD schemes based on the Correction Function Method (CFM) for Maxwell's interface problems with discontinuous coefficients and complex interfaces. The key idea of the CFM is to model the correction function near an…
In this paper we construct high order numerical methods for solving third and fourth orders nonlinear functional differential equations (FDE). They are based on the discretization of iterative methods on continuous level with the use of the…
In this manuscript, we propose newly-derived exponential quadrature rules for stiff linear differential equations with time-dependent fractional sources in the form $h(t^r)$, with $0<r<1$ and $h$ a sufficiently smooth function. To construct…
In this paper, we introduce second order and fourth order space discretization via finite difference implementation of the finite element method for solving Fokker-Planck equations associated with irreversible processes. The proposed…
In this paper, we develop a framework to construct energy-preserving methods for multi-components Hamiltonian systems, combining the exponential integrator and the partitioned averaged vector field method. This leads to numerical schemes…
This paper presents compact, symmetric, and high-order finite difference methods (FDMs) for the variable Poisson equation on a $d$-dimensional hypercube. Our scheme produces a symmetric linear system: an important property that does not…
We introduce the multivariate decomposition finite element method (MDFEM) for solving elliptic PDEs with uniform random diffusion coefficients. We show that the MDFEM can be used to reduce the computational complexity of estimating the…
To address the sensitivity of parameters and limited precision for physics-informed extreme learning machines (PIELM) with common activation functions, such as sigmoid, tangent, and Gaussian, in solving high-order partial differential…
We study the exponential stability of evolutionary equations. The focus is laid on second order problems and we provide a way to rewrite them as a suitable first order evolutionary equation, for which the stability can be proved by using…