22 papers · ranked by Valyu relevance
Ming Tian Xu
At present, only some special differential equations have explicit analytical solutions. In general, no one thinks that it is possible to analytically find the exact solution of nonlinear equations. In this article based on the idea that the numerical scheme with zero truncation error can give rise to exact solution, a…
Andrei D. Polyanin
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied mathematics and mathematical physics, based on a special transformation with an…
Bilige Sudao, Xiaomin Wang, Vanesa Magar
In this paper, a generalized simplest equation method is proposed to seek exact solutions of nonlinear evolution equations (NLEEs). In the method, we chose a solution expression with a variable coefficient and a variable coefficient ordinary differential auxiliary equation. This method can yield a Bäcklund…
Matthew J Simpson, Jesse A Sharp, Liam C Morrow, Ruth E Baker
Embryonic development involves diffusion and proliferation of cells, as well as diffusion and reaction of molecules, within growing tissues. Mathematical models of these processes often involve reaction–diffusion equations on growing domains that have been primarily studied using approximate numerical solutions.…
Tahir Shahzad, Muhammad Ozair Ahmed, Muhammad Zafarullah Baber, Nauman Ahmed + 2 more
'Nauman Ahmed' 'Ali Akgül' 'Sayed M. El Din'] In this study, the Sobolev-type equation is considered analytically to investigate the solitary wave solutions. The Sobolev-type equations are found in a broad range of fields, such as ecology, fluid dynamics, soil mechanics, and thermodynamics. There are two novel…
Litao Gai, Sudao Bilige, Yingmo Jie
In this paper, we successfully obtained the exact solutions and the approximate analytic solutions of the (2 + 1)-dimensional KP equation based on the Lie symmetry, the extended tanh method and the homotopy perturbation method. In first part, we obtained the symmetries of the (2 + 1)-dimensional KP equation based on…
Matthew J. Simpson
Many processes during embryonic development involve transport and reaction of molecules, or transport and proliferation of cells, within growing tissues. Mathematical models of such processes usually take the form of a reaction–diffusion partial differential equation (PDE) on a growing domain. Previous analyses of such…
Kamruzzaman Khan, M. Ali Akbar, H. Koppelaar
Exact solutions of nonlinear partial differential equations (NPDEs) are obtained via the enhanced (G′/G)-expansion method. The method is subsequently applied to find exact solutions of the Drinfel'd-Sokolov-Wilson (DSW) equation and the (2+1)-dimensional Painlevé integrable Burgers (PIB) equation. The efficiency of…
Arindam Ghosh, Sarit Maitra, A. Roy Chowdhury
In this work the longitudinal wave equation through magneto-electro-elastic circular rod is studied analytically. Painlev´e test is performed to check integrability of the equation. Exact solitary wave solutions are found by homogeneous balance method and Tanh method and are plotted using suitable values of physical…
Nikolay K. Vitanov, Zlatinka I. Dimitrova, Kaloyan N. Vitanov
The goal of this article is to discuss the Simple Equations Method (SEsM) for obtaining exact solutions of nonlinear partial differential equations and to show that several well-known methods for obtaining exact solutions of such equations are connected to SEsM. In more detail, we show that the Hirota method is…
Eugene Christo V R, Christoph Robert Meinecke, Bert Nitzsche, Roman Lyttleton + 5 more
Network-based biocomputing (NBC) presents an energy-efficient, parallel computing approach for solving nondeterministic polynomial time (NP) complete problems by leveraging motor-driven cytoskeletal filaments that explore all possible solutions through nanofabricated networks in a massively parallel fashion. However…
Justine Dattani, Mauricio Barahona
Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells with time-varying (stochastic or deterministic) transcription and degradation…
Bin Zheng
We extend the Exp-function method to fractional partial differential equations in the sense of modified Riemann-Liouville derivative based on nonlinear fractional complex transformation. For illustrating the validity of this method, we apply it to the space-time fractional Fokas equation and the nonlinear fractional…
Dana Seilova, Olzhas Akbayev, Yerkezhan Assylbek, Akzhan Bakibayeva
In physical research of nonlinear waves spread in waveguides, it is necessary to take into account the interaction of waveguides with external environment (Berezhkoyskii, 2011). Therefore, the possibility of energy exchange through the outer surface of waveguides, is also should be taken into account (Berezhkoyskii…
harry gray
The matrix exponential method as implemented in MATLAB is demonstrated as a facile tool for solving the time-dependent concentrations of an arbitrary chemically reactive network modelled as a coupled linear system of first-order differential equations. The method is used to verify a 10 species network incorporating…
Qianxiang Ai, Joshua Schrier
In a recent paper in this journal (Chem. Mater. 2022, 34, 2545-2552), Twyman et al. studied the environmental stability of crystals by introducing a greedy heuristic algorithm for determining possible oxidation reactions. We show how the problem can be solved exactly, with less code and comparable computational time by…
Authors not listed
A method has been introduced to derive the solution of the time-independent Schrodinger equation for the simple harmonic oscillator. A trial solution has been chosen as the product of the divergent part of the approximate asymptomatic solution of the Schrodinger equation and an unknown function. By inserting this trial…
Ali Yousefi, Mohammad Reza Rezaei, Kensuke Arai, Loren M. Frank + 1 more
There is an increasing demand for a computationally efficient and accurate point process filter solution for real-time decoding of population spiking activity in multidimensional spaces. Real-time tools for neural data analysis, specifically real-time neural decoding solutions open doors for developing experiments in a…
Authors not listed
Triple Tube Heat Exchangers (TTHEs) are suitable equipment for thick viscosity products, with or without particulates, with various applications in the food and pharmaceutical industries. Although less commonly used than Double Tube Heat Exchangers (DTHEs), TTHEs often perform better than DTHEs. However, in the case of…
Daiyuan Zhang
All the theories and methods proposed in this paper are my original innovations. On the basis of the new mathematical expansion I proposed in 2014, this paper presents a general method for solving linear ordinary differential equations. Different from traditional known methods, this paper deals with a completely new…
Authors not listed
The SCF part of the HF-SCF method is responsible for finding the ground state as the global minimum of the one-determinant approximation of the electronic energy, which is a 4th order multivariable polynomial of the LCAO coefficients and Lagrange multipliers. In this work we replace this SCF part with algebraic…
Authors not listed
The polarizable continuum model (PCM) is a computationally efficient way to incorporate dielectric boundary conditions into electronic structure calculations, via a boundary-element reformulation of Poisson's equation. This transformation is only rigorously valid for an isotropic dielectric medium. To simulate…