Related papers: Exact Solutions of the Cubic-Quintic Duffing Equat…
We consider a second-order equation of Duffing type. Bounds for the derivative of the restoring force are given which ensure the existence and uniqueness of a periodic solution. Furthermore, the unique periodic solution is asymptotically…
In this article, we deal with the efficient computation of the Wright function in the cases of interest for the expression of solutions of some fractional differential equations. The proposed algorithm is based on the inversion of the…
An analysis of a fractional cubic differential equation is presented, which is a generalization of different versions of fractional logistic equations, in order to obtain simpler numerical methods that globalize and extend the results…
Using Painlev\'e analysis, the Hirota multi-linear method and a direct ansatz technique, we study analytic solutions of the (1+1)-dimensional complex cubic and quintic Swift-Hohenberg equations. We consider both standard and generalized…
We provide an exact algorithm to solve the log-linear continuous (fractional) knapsack problem. The algorithm is based on two lemmas that follow from the application of weak duality theorem and complementary slackness theorem to the linear…
Cubic and quartic non-autonomous differential equations with continuous piecewise linear coefficients are considered. The main concern is to find the maximum possible multiplicity of periodic solutions. For many classes, we show that the…
In this paper, we discuss foliations by real curves. We investigate differential equations which are modifications of du/dx = v along leaves. Our focus is on having a solution operator so that u is continuous if v is continuous.
We present an algorithm for solving the self-consistency equations of the dynamical mean-field theory (DMFT) with high precision and efficiency at low temperatures. In each DMFT iteration, the impurity problem is mapped to an auxiliary…
In this paper, we develop a new deformation and generalization of the Natural integral transform based on the conformable fractional $q$-derivative. We obtain transformation of some deformed functions and apply the transform for solving…
Standard density functional approximations often give questionable results for odd-electron radical complexes, with the error typically attributed to self-interaction. In density corrected density functional theory (DC-DFT), certain classes…
Matched layers are commonly used in numerical simulations of wave propagation to model (semi-)infinite domains. Attenuation functions describe the damping in layers, and provide a matching of the wave impedance at the interface between the…
This article proposes a novel approach for determining exact solutions to nonlinear ordinary differential equations. The recommended iterative method provides the solution via a rapidly converging series that readily approaches a closed…
Approximating periodic solutions to the coupled Duffing equations amounts to solving a system of polynomial equations. The number of complex solutions measures the algebraic complexity of this approximation problem. Using the theory of…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Finite element approximation to a decoupled formulation for the quad--curl problem is studied in this paper. The difficulty of constructing elements with certain conformity to the quad--curl problems has been greatly reduced. For convex…
This article studies a direct numerical approach for fractional advection-diffusion equations (ADEs). Using a set of cubic trigonometric B-splines as test functions, a differential quadrature (DQ) method is firstly proposed for the 1D and…
We develop a Frank-Wolfe algorithm with corrective steps, generalizing previous algorithms including blended conditional gradients, blended pairwise conditional gradients, and fully-corrective Frank-Wolfe. For this, we prove tight…
This article introduces an intuitive function MY that simplifies solving cubic equations without venturing into the complex space. To many, it's quite strange that cubic root(s) are expressed using trigonometric functions in the…
In this work an extended elliptic function method is proposed and applied to the generalized shallow water wave equation. We systematically investigate to classify new exact travelling wave solutions expressible in terms of quasi-periodic…
The purpose of this paper is to solve the 0-1 $k$-item quadratic knapsack problem $(kQKP)$, a problem of maximizing a quadratic function subject to two linear constraints. We propose an exact method based on semidefinite optimization. The…