26 papers · ranked by Valyu relevance
Davoud Mirzaei
Contents 1 An introduction to ODEs 1 1.1 Modelling with ODEs: a funny example . . . . . . . . . . . . . . . . . . . 4 1.2 Higher order ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.3 First order system of ODEs . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1.4 Stability of solutions . .…
A. K. Alekseev, А. Е. Бондарев
The solution in sense of Prager&Synge is the alternative to the commonly used notion of the numerical solution, which is considered as a limit of grid functions at mesh refinement. Prager&Synge solution is defined as a hypersphere containing the projection of the true solution of the system of partial differentiation…
Alexander Hvatov, Tatiana Tikhonova
The numerical methods for differential equation solution allow obtaining a discrete field that converges towards the solution if the method is applied to the correct problem. Nevertheless, the numerical methods have the restricted class of the equations, on which the convergence with a given parameter set or range is…
Malgorzata Klimek, Mariusz Ciesielski, Tomasz Blaszczyk, Praveen Agarwal + 5 more
'Praveen Agarwal' 'Carlo Cattani' 'Thiab Taha' 'Shaher Momani' 'Juan Luis García Guirao' 'António Mendes Lopes'] In this paper, we study the fractional Sturm-Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space.…
Sam Motsoka Rametse, Sheldon Herbst
Accurate and stable numerical simulation of epidemic dynamics is essential for translating mathematical models into reliable computational tools for public health. The Susceptible–Infectious–Recovered (SIR) model remains a cornerstone of mathematical epidemiology, yet the robustness of its numerical treatment strongly…
Salima Kouser, Shafiq Ur Rehman, Yasser Elmasry, Waqar Azeem Khan + 3 more
'Fayyaz Ahmad' 'Hamza Khan' 'B. Omkar Lakshmi Jagan'] The Newton method is a classical method for solving systems of nonlinear equations and offers quadratic convergence. The order of convergence of the Newton method is optimal as it requires one evaluation for the system of nonlinear equations and the second for the…
Yuji Masutomi, Kazuhiko Kobayashi
The photosynthesis–transpiration–stomatal conductance (A_n_–E–g_s_) model framework is widely used for estimating photosynthesis, transpiration, and stomatal conductance in plants. The model equations are solved by numerical iteration, and the converged model values are deemed the solution. However, there has been no…
Giuseppe de Alteriis, Enrico Cataldo, Alberto Mazzoni, Calogero Maria Oddo
The Izhikevich artificial spiking neuron model is among the most employed models in neuromorphic engineering and computational neuroscience, due to the affordable computational effort to discretize it and its biological plausibility. It has been adopted also for applications with limited computational resources in…
Lionel Dupuy, Matthias Mimault, Mariya Ptashnyk
Movement is critical for bacterial species inhabiting soils because nutrient availability is limited and heterogeneously distributed both in space and time. Recent live microscopy experiments show that bacteria form flocks when navigating through porous medium, and complex cell-cell interactions may be required to…
Daphne Nesenberend, Arjen Doelman, Frits Veerman
The exact mechanisms behind many morphogenic processes are still a mystery. Mechanical cues, such as curvature, play an important role when tissue or cell shape is formed. In this work, we derive and analyze a mechanochemical model. This particular spatially one-dimensional model describes the deformation of a tissue-…
Zai, Ling-Zhe, Guo, Lei-Lei + 1 more
Solving nonlinear algebraic equations is a fundamental but challenging problem in scientific computations and also has many applications in system engineering. Though traditional iterative methods and modern optimization algorithms have exerted effective roles in addressing certain specific problems, there still exist…
Marius-F. Danca, Quanmin Zhu, Giuseppe Fusco, Jing Na + 1 more
In this paper, the solutions of a class of switch dynamical systems are investigated. The right-hand side of the underlying equations is discontinuous with respect to the state variable. The discontinuity is represented by jump discontinuous functions such as signum or Heaviside functions. In this paper, a novel…
Kushal Dhar Dwivedi, Anup Singh
Order Differential Equations Authors: ['Kushal Dhar Dwivedi' 'Anup Singh'] Abstract In this paper, the authors propose the utilization of Fibonacci Neural Networks (FNN) for solving arbitrary order differential equations. The FNN architecture comprises input, middle, and output layers, with various degrees of Fibonacci…
Azhar Iqbal Kashif Butt, Nehad Ali Shah, Waheed Ahmad, Thongchai Botmart + 1 more
'Thongchai Botmart' 'Naeed Ahmad'] In this paper, we consider an isothermal glass tube drawing model consisting of three coupled nonlinear partial differential equations. The steady-state solution of this model is required in order to investigate its stability. With the given initial and boundary conditions, it is not…
Ðinh Nho Hào, Thuy T. Le, Loc H. Nguyen
The objective of this article is to introduce a novel technique for computing numerical solutions to the nonlinear inverse heat conduction problem. This involves solving nonlinear parabolic equations with Cauchy data provided on one side Γ of the boundary of the computational domain Ω. The key step of our proposed…
MARCO TODISCO
Determining the distribution of multiple chemical species at equilibrium for a given system is a common problem that must be routinely addressed by scholars. While simple systems consisting of a few species and reactions can be solved manually, most of these problems require the definition and solution of higher-order…
V.V. Kryzhniy
This paper presents a universal numerical scheme tailored for tackling linear integral, integro-differential, and both initial and boundary value problems of ordinary differential equations. The numerical scheme is readily adapted for resolving ill-posed problems. Central to our approach is high-degree…
Jinxing Liu, Muhammad Nadeem, M. S. Osman, Yahya Alsayaad
Many scientific phenomena are linked to wave problems. This paper presents an effective and suitable technique for generating approximation solutions to multi-dimensional problems associated with wave propagation. We adopt a new iterative strategy to reduce the numerical work with minimum time efficiency compared to…
Ray Zirui Zhang, Christopher E. Miles, Xiaohui Xie, John S. Lowengrub
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with respect to the PDE parameters. At the lower level, we train a neural network to…
Daniel T. Birdsell, Benjamin M. Adams, Jonathan D. Ogland-Hand, Jeffrey M. Bielicki + 2 more
Geothermal electricity generation may play a role in reducing greenhouse gas emissions and addressing climate change in a cost-effective manner. Reservoir equations for pressure and temperature must be coupled to a power cycle model to calculate electricity generation from a geothermal power plant. This work focuses on…
Jie Liu, Fuzhang Wang, Sohail Nadeem, Abderrahim Wakif
The aim of this paper is to introduce a novel category of radial basis functions that incorporate smoothing techniques. Initially, we employ the power augmented and shape parameter schemes to create the radial basis functions. Subsequently, we apply the newly-constructed radial basis functions using the traditional…
Michele Nottoli, Michael F. Herbst, Aleksandr Mikhalev, Abhinav Jha + 2 more
Polarizable continuum solvation models are popular in both, quantum chemistry and in biophysics, though typically with different requirements for the numerical methods. However, the recent trend of multiscale modeling can be expected to blur field-specific differences. In this regard, numerical methods based on domain…
Authors not listed
Moving bed reactors (MBRs) are widely used in various industrial processes, making the development of mathematical models crucial for their design, optimization, and control. This study presents a semi-analytical solution (SAS) for a lumped parameter kinetic and heat transfer model of a tubular MBR, where a first-order…
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…
Mohammed H. Ali, Hamdy M. Ahmed, Soliman Alkhatib, M. Elsaid Ramadan + 2 more
In this study, a high-order stochastic nonlinear Schrödinger equation (SNLSE) with weak non-local nonlinearity in a non-Kerr law medium is investigated. This model describes the propagation of solitons in nonlinear optical fibers under stochastic effects and higher-order nonlinear interactions. To obtain analytical…
Authors not listed
Rapid and robust simulation of chemical processes is critical to conduct process design, optimization, techno-economic analysis, and sustainability analysis. Yet, efficiently solving simulation models remains a challenge due to the highly coupled and nonlinear nature of the underlying algebraic equations that capture…