17 papers · ranked by Valyu relevance
A. Ghose Choudhury, Partha Guha, Nikolay A. Kudryashov
The study of higher-order Painlev´e equations is interesting from the mathematical point of view because of the possibility of existence of new transcendental functions beyond the six Painlev´e transcendents. In addition such higher-order Painlev´e often have interesting physical and mathematical applications. For…
Mohammed S. Mechee, Mohammed Mahmood Salih
Background In this paper, we focus on deriving an efficient method for solving ordinary differential equations (ODEs) of sixth order, and then, we modify the proposed method for solving fractional differential equations (FDEs). Methods The methodology of this paper used the approach of derivation of implicit numerical…
João Henrique Andrade, Juncheng Wei
We classify entire positive singular solutions to a family of critical sixth order equations in the punctured space with a non-removable singularity at the origin. More precisely, we show that when the origin is a non-removable singularity, solutions are given by a singular radial factor times a periodic solution to a…
S. Roy Choudhury, Ranses Alfonso Rodriguez
New third- and fourth-order Lagrangian hierarchies are derived in this paper. The free coefficients in the leading terms satisfy the most general differential geometric criteria currently known for the existence of a variational formulation, as derived by solution of the full inverse problem of the Calculus of…
Ding-jiang Huang, Qinmin Yang, Shuigeng Zhou
Using group theoretical methods, we analyze the generalization of a one-dimensional sixth-order thin film equation which arises in considering the motion of a thin film of viscous fluid driven by an overlying elastic plate. The most general Lie group classification of point symmetries, its Lie algebra, and the…
Mina M. Fahim, Hamdy M. Ahmed, K. A. Dib, Islam Samir
In this work, a sixth-order extension of the nonlinear Schrödinger equation (NLSE) within its integrable hierarchy is investigated to model higher-order nonlinear and dispersive effects relevant to optical fiber systems and nonlinear wave propagation. By employing the Improved Modified Extended Tanh Function Method, a…
W. M. Abd-Elhameed
This paper is concerned with deriving some new formulae expressing explicitly the high-order derivatives of Jacobi polynomials whose parameters difference is one or two of any degree and of any order in terms of their corresponding Jacobi polynomials. The derivatives formulae for Chebyshev polynomials of third and…
Tatsuya Hosoi, Hidetaka Sakai
The sixth Painlev´e equation is a basic equation among the non-linear differential equations with three fixed singularities, corresponding to Gauss's hypergeometric differential equation among the linear differential equations. It is known that 2nd order Fuchsian differential equations with three singular points are…
V. Murugesh, M. Priyadharshini, Yogesh Kumar Sharma, Umesh Kumar Lilhore + 4 more
'Umesh Kumar Lilhore' 'Roobaea Alroobaea' 'Hamed Alsufyani' 'Abdullah M. Baqasah' 'Sarita Simaiya'] In this paper, the author introduces the Neural-ODE Hybrid Block Method, which serves as a direct solution for solving higher-order ODEs. Many single and multi-step methods employed in numerical approximations lose their…
Dulfikar Jawad Hashim, Mohammed Jasim Mohammed Alfahdawi
This study tackles the challenge of obtaining highly accurate approximate solutions for nonlinear fractional differential equations, which often lack exact solutions due to their inherent complexity. A unified perturbation framework is proposed based on homotopy topology theory, enabling multiple formulations depending…
Philipp Städter, Yannik Schälte, Leonard Schmiester, Jan Hasenauer + 1 more
Ordinary differential equation (ODE) models are a key tool to understand complex mechanisms in systems biology. These models are studied using various approaches, including stability and bifurcation analysis, but most frequently by numerical simulations. The number of required simulations is often large, e.g., when…
Authors not listed
Two kinetic schemes of the general modifier mechanism have been analysed in a quasi-steady state approximation, assuming that the reaction product concentration is negligible (a natural assumption for the initial rate method) and without additional simplifying assumptions. The characteristic equations have been…
Margaret P. Chapman, Claire J. Tomlin
Ordinary differential equations (ODEs) provide a classical framework to model the dynamics of biological systems, given temporal experimental data. Qualitative analysis of the ODE model can lead to further biological insight and deeper understanding compared to traditional experiments alone. Simulation of the model…
Paul Stapor, Fabian Fröehlich, Jan Hasenauer
Parameter estimation methods for ordinary differential equation (ODE) models of biological processes can exploit gradients and Hessians of objective functions to achieve convergence and computational efficiency. However, the computational complexity of established methods to evaluate the Hessian scales linearly with…
Sam Subbey, Anna S. Frank, Melanie Kobras
This paper uses a Lotka-Volterra (predator-prey) modeling framework to investigate the dynamical link between the biomass of an empirical predator, and that of its prey. We use a system of ordinary (ODE) differential equations to describe the system dynamics, and derive theoretical conditions for stability, in terms of…
Paul Stapor, Leonard Schmiester, Christoph Wierling, Bodo M.H. Lange + 2 more
Quantitative dynamical models are widely used to study cellular signal processing. A critical step in modeling is the estimation of unknown model parameters from experimental data. As model sizes and datasets are steadily growing, established parameter optimization approaches for mechanistic models become…
Jonathan Oesterle, Nicholas Krämer, Philipp Hennig, Philipp Berens
Understanding neural computation on the mechanistic level requires models of neurons and neuronal networks. To analyze such models one typically has to solve coupled ordinary differential equations (ODEs), which describe the dynamics of the underlying neural system. These ODEs are solved numerically with deterministic…