Related papers: The explicit Laplace transform for the Wishart pro…
We give an algorithm for reversion of formal power series, based on an efficient way to implement the Lagrange inversion formula. Our algorithm requires $O(n^{1/2}(M(n) + MM(n^{1/2})))$ operations where $M(n)$ and $MM(n)$ are the costs of…
A formula of Doetsch ({\em Math. Zeitschr.} {\bf 42}, 263 (1937)) is generalized and used to numerically invert the one-sided Laplace transform ${\hat C}(\beta)$. The necessary input is only the values of ${\hat C}(\beta)$ on the positive…
The Laplace transform of the first passage time density of the Ornstein--Uhlenbeck process for a constant threshold contains a ratio of two parabolic cylinder functions for which no analytical inversion formula is available. Recently…
In this paper, we propose a numerical method of computing an integral whose integrand is a slowly decaying oscillatory function. In the proposed method, we consider a complex analytic function in the upper-half complex plane, which is…
In this article, a new modified Laplace-Fourier method is developed in order to obtain the solutions of linear neutral delay differential equations. The proposed method provides a more accurate solution than the one provided by the pure…
Our paper introduces a novel method for calculating the inverse $\mathcal{Z}$-transform of rational functions. Unlike some existing approaches that rely on partial fraction expansion and involve dividing by $z$, our method allows for the…
This paper deals with the equation $-\Delta u+\mu u=f$ on high-dimensional spaces $\mathbb{R}^m$, where the right-hand side $f(x)=F(Tx)$ is composed of a separable function $F$ with an integrable Fourier transform on a space of a dimension…
One of the main objectives of science is the recognition of a general pattern in a particular phenomenon in some particular regime. In this work, this is achieved with the analytical expression for the optimal protocol that minimizes the…
We give a new procedure for generalized factorization and construction of the complete solution of strictly hyperbolic linear partial differential equations or strictly hyperbolic systems of such equations in the plane. This procedure…
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…
Burgers' equation with fixed Dirichlet boundary conditions is considered on generic bounded intervals. By using the Hopf-Cole transformation and the exact operational solution recently established for linear reaction-diffusion equations…
Let $K$ be a number field, and let $K(x_1,...,x_d)$ be the field of rational fractions in the variables $x_1,...,x_d$. In this paper, we introduce two kinds of Laplace transform adapted to solutions of the differential…
We present two new proofs of the exchange theorem for the Laplace transformation of vector-valued distributions. We then derive an explicit solution to the Dirichlet problem of the polyharmonic operator in a half-space. Finally, we obtain…
We explore two classes of exponential integrators in this letter to design nonlinear Fourier transform (NFT) algorithms with a desired accuracy-complexity trade-off and a convergence order of $4$ on an equispaced grid. The integrating…
Exact recursion formulas for mixed moments of four fundamental random matrix ensembles are derived. The reason such recursive formulas are possible is closely related to properties of polygon gluings studied by Harer and Zagier as well as…
We intend to realize the step-up and step-down operators of the potential $V(x)=V_{1}e^{2\beta x}+V_{2}e^{\beta x}$. It is found that these operators satisfy the commutation relations for the SU(2) group. We find the eigenfunctions and the…
We develop the Fourier-Laplace Inversion of the Perturbation Theory (FLIPT), a novel numerically exact "black box" method to compute perturbative expansions of the density matrix with rigorous convergence conditions. Specifically, the FLIPT…
This note discusses Routh reduction for hybrid time-dependent mechanical systems. We give general conditions on whether it is possible to reduce by symmetries a hybrid time-dependent Lagrangian system extending and unifying previous results…
Cell collective migration plays a crucial role in a variety of physiological processes. In this work, we propose the Runge-Kutta random feature method to solve the nonlinear and strongly coupled multiphase flow problems of cells, in which…
Consistent initialization of the Laplace transform has been a fundamental and long-standing issue. The consistency of the L- approach has been questioned, yet it is a popular approach since the L+ approach requires a priori computation of…