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We analyze the asymptotic properties a special solution of the $(3,4)$ string equation, which appears in the study of the multicritical quartic $2$-matrix model. In particular, we show that in a certain parameter regime, the corresponding…
The Asymptotic Iteration Method (AIM) is a technique for solving analytically and approximately the linear second-order differential equation, especially the eigenvalue problems that frequently appear in theoretical and mathematical…
The renormalization method based on the Taylor expansion for asymptotic analysis of differential equations is generalized to difference equations. The proposed renormalization method is based on the Newton-Maclaurin expansion. Several basic…
We study asymptotic solutions to a singularly-perturbed, period-2 Toda lattice and use exponential asymptotics to examine `nanoptera', which are nonlocal solitary waves with constant-amplitude, exponentially small wave trains. With this…
In this paper, we derive new asymptotic expansions for the solutions of higher order elliptic equations in the presence of small inclusions. As a byproduct, we derive a topological derivative based algorithm for the reconstruction of…
A two-step method for solving planar Laplace problems via rational approximation is introduced. First complex rational approximations to the boundary data are determined by AAA approximation, either globally or locally near each corner or…
We apply the asymptotic iteration method (AIM) [J. Phys. A: Math. Gen. 36, 11807 (2003)] to solve new classes of second-order homogeneous linear differential equation. In particular, solutions are found for a general class of eigenvalue…
Empirical results show that Anderson acceleration (AA) can be a powerful mechanism to improve the asymptotic linear convergence speed of the Alternating Direction Method of Multipliers (ADMM) when ADMM by itself converges linearly. However,…
We introduce a new algorithm for approximation by rational functions on a real or complex set of points, implementable in 40 lines of Matlab and requiring no user input parameters. Even on a disk or interval the algorithm may outperform…
Asymptotic formula is derived for the behavior of the fundamental solution of the second-order elliptic self-adjoint operator with a piecewise-smooth coefficient in front of the senior derivatives near the discontinuity surface of the…
A system of linear differential equations with oscillatory decreasing coefficients is considered. The coefficients has the form $t^{-\alpha}a(t)$,~$\alpha>0$, where $a(t)$ is trigonometric polynomial with an arbitrary set of frequencies.…
Stokes perturbative solution of the nonlinear (boundary value dependent) surface gravity wave problem is known to provide results of reasonable accuracy to engineers in estimating the phase speed and amplitudes of such nonlinear waves. The…
We study homoclinic snaking of one-dimensional, localised states on two-dimensional, bistable lattices via the method of exponential asymptotics. Within a narrow region of parameter space, fronts connecting the two stable states are pinned…
We consider the Helmholtz equation in an angular sector partially covered by a homogeneous layer of small thickness, denoted $\varepsilon$. We propose in this work an asymptotic expansion of the solution with respect to $\varepsilon$ at any…
In cosmology an important role is played by homogeneous and isotropic solutions of the Einstein-Euler equations and linearized perturbations of these. This paper proves results on the asymptotic behaviour of scalar perturbations both in the…
Complicated physical problems usually are solved by resorting to perturbation theory leading to solutions in the form of asymptotic series in powers of small parameters. However, finite, and even large values of the parameters often are of…
Sequential data collection has emerged as a widely adopted technique for enhancing the efficiency of data gathering processes. Despite its advantages, such data collection mechanism often introduces complexities to the statistical inference…
We investigate geometric aspects of co-equational parametric resurgence, by studying physical problems whose formal asymptotic solutions give rise to Borel transforms lying on an algebraic curve. This perspective allows us to elucidate…
This paper is part of a series of papers in which the asymptotic theory and appropriate symbolic computer code are developed to compute the asymptotic expansion of the solution of an n-th order ordinary differential equation. The paper…
Recently, symbolic regression (SR) has demonstrated its efficiency for discovering basic governing relations in physical systems. A major impact can be potentially achieved by coupling symbolic regression with asymptotic methodology. The…