相关论文: Numerical approximations for population growth mod…

In this paper we derive the closed-form solutions for the Lucas-Uzawa growth model with the aid of the partial Hamiltonian approach and then compare our results with those derived by the classical approach \cite{chil}. The partial…

The classical Lotka-Volterra predator-prey system is often used in species competition modeling. An exact, closed-form solution is derived when the natural growth rate of the prey species and decay rate of the predators are equal in…

The Gerber-Shiu function is a classical research topic in actuarial science.However, exact solutions are only available in the literature for very specific cases where the claim amounts follow distributions such as the exponential…

We consider rank-1 lattices for integration and reconstruction of functions with series expansion supported on a finite index set. We explore the connection between the periodic Fourier space and the non-periodic cosine space and Chebyshev…

We present the Fast Chebyshev Transform (FCT), a fast, randomized algorithm to compute a Chebyshev approximation of functions in high-dimensions from the knowledge of the location of its nonzero Chebyshev coefficients. Rather than sampling…

We develop a partial Hamiltonian framework to obtain reductions and closed-form solutions via first integrals of current value Hamiltonian systems of ordinary differential equations (ODEs). The approach is algorithmic and applies to many…

In the classical Lotka-Volterra population models, the interacting species affect each other's growth rate. We propose an alternative model, in which the species affect each other through the limitation coefficients, rather then through the…

This paper is concerned with the numerical solution for a class of nonlinear weakly singular Volterra integral equation of the first kind. The existence and uniqueness issue of the nonlinear Abel integral equations is studied completely. An…

This paper presents an efficient spectral method for solving the fractional Fredholm integro-differential equations. The non-smoothness of the solutions to such problems leads to the performance of spectral methods based on the classical…

The paper was suggested by a brief note of the second author about the application of the Hubbert curve to predict decay of resource exploitation. A further suggestion came from the interpretation of the Hubbert curve in terms of a specific…

We study the interplay between population imbalance in a two-component fermionic system and nearest-neighbor interaction using matrix product states method. Our analysis reveals the existence of a new type of…

We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…

The Kubo formula is a cornerstone in our understanding of near-equilibrium transport phenomena. While conceptually elegant, the application of Kubo's linear-response theory to interesting problems is hindered by the need for algorithms that…

A series of problems in different fields such as physics and chemistry are modeled by differential equations. Differential equations are divided into partial differential equations and ordinary differential equations which can be linear or…

We introduce a new algorithm which we call the {Rational Hybrid Monte Carlo} Algorithm (RHMC). This method uses a rational approximation to the fermionic kernel together with a noisy Kennedy-Kuti acceptance step to give an efficient…

Recently, the efficient numerical solution of Hamiltonian problems has been tackled by defining the class of energy-conserving Runge-Kutta methods named Hamiltonian Boundary Value Methods (HBVMs). Their derivation relies on the expansion of…

This paper presents a computationally efficient model predictive control formulation that uses an integral Chebyshev collocation method to enable rapid operations of autonomous agents. By posing the finite-horizon optimal control problem…

Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory…

Interior eigenvalue problems for large-scale sparse Hermitian matrices are fundamental in computational science. We propose an adaptive polynomial filtering strategy based on Chebyshev expansion of a step function, integrated into a…

Models of Stock Recruitment Relationships (SRRs) are often used to predict fish population dynamics. Commonly used SRRs include the Ricker, Beverton-Holt, and Cushing functional forms, which differ primarily by the degree of density…