21 papers · ranked by Valyu relevance
Udaya Pratap Singh
This work investigates a new approach to find closed form analytical approximate solution of linear initial value problems. Classical Bernoulli polynomials have been used to derive a finite set of orthonormal polynomials and a finite operational matrix to simplify derivatives of dependent variable. These orthonormal…
Oscar A. Barraza
The purpose of this note is to present a formulation of a given nonlinear ordinary differential equation into an equivalent system of linear ordinary differential equations. It is evident that the easiness of a such procedure would be able to open a new way in order to calculate or approximate the solution of an…
Ying Wen, Temuer Chaolu, Xiangsheng Wang, Shou-Fu Tian
To combine a feedforward neural network (FNN) and Lie group (symmetry) theory of differential equations (DEs), an alternative artificial NN approach is proposed to solve the initial value problems (IVPs) of ordinary DEs (ODEs). Introducing the Lie group expressions of the solution, the trial solution of ODEs is split…
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…
Asia Kanwal, Salah Boulaaras, Ramsha Shafqat, Bilal Taufeeq + 1 more
'Mati ur Rahman'] The creation of an explicit finite difference scheme with the express purpose of resolving initial boundary value issues with linear and semi-linear variable-order temporal fractional properties is presented in this study. The rationale behind the utilization of the Caputo derivative in this scheme…
Shixiong Wang, Jianhua He, Chen Wang, Xitong Li
Many Engineering Problems could be mathematically described by Final Value Problem, which is the inverse problem of Initial Value Problem. Accordingly, the paper studies the final value problem in the field of ODE problems and analyses the differences and relations between initial and final value problems. The more…
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…
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…
Mehmet Pakdemirli
The recently developed perturbation iteration method is applied to boundary layer type singular problems for the first time. As a preliminary work on the topic, the simplest algorithm of PIA(1,1) is employed in the calculations. Linear and nonlinear problems are solved to outline the basic ideas of the new solution…
Hamid Semiyari
In this article we introduce a simple straightforward and powerful method involving symbolic manipulation, Picard iteration, and auxiliary variables for approximating solutions of partial differential boundary value problems. The method is easy to implement, computationally efficient, and it is highly accurate. The…
Yuanheng Wang, Barrira Jurrat, Muddasir Ejaz, Muhammad Azeem + 2 more
'M. I. Elashiry' 'Rehana Naz'] In this paper, the existence and uniqueness of solution for a fractional differential model involving well-posed boundary conditions and implicit fractional differential equation is considered. The desired goals are achieved by using Banach contraction principle and Scheafer’s fixed point…
Suheel Abdullah Malik, Ijaz Mansoor Qureshi, Muhammad Amir, Ihsanul Haq
'Ihsanul Haq'] We present a hybrid heuristic computing method for the numerical solution of nonlinear singular boundary value problems arising in physiology. The approximate solution is deduced as a linear combination of some log sigmoid basis functions. A fitness function representing the sum of the mean square error…
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…
Sungho Shin, Ophelia Venturelli, Victor M. Zavala
We present a nonlinear programming (NLP) framework for the scalable solution of parameter estimation problems that arise in dynamic modeling of biological systems. Such problems are computationally challenging because they often involve highly nonlinear and stif differential equations as well as many experimental data…
Alejandro F. Villaverde, Fabian Fröhlich, Daniel Weindl, Jan Hasenauer + 1 more
Mechanistic kinetic models usually contain unknown parameters, which need to be estimated by optimizing the fit of the model to experimental data. This task can be computationally challenging due to the presence of local optima and ill-conditioning. While a variety of optimization methods have been suggested to…
Brahim Benhammouda
The solution of higher-index Hessenberg differential-algebraic equations (DAEs) is of great importance since this type of DAEs often arises in applications. Higher-index DAEs are known to be numerically and analytically difficult to solve. In this paper, we present a new analytical method for the solution of two…
Niklas Neubrand, Timo Rachel, Tim Litwin, Jens Timmer + 2 more
Systems biology strives to unravel the complex dynamics of cellular processes, often with the help of ordinary differential equations (ODEs). However, the sparsity of measured data and the strong non-linearity of common ODEs introduce severe numerical problems in typical modeling tasks. This gave rise to the…
Helge Hass, Carolin Loos, Elba Raimundez Alvarez, Jens Timmer + 2 more
Dynamic models are used in systems biology to study and understand cellular processes like gene regulation or signal transduction. Frequently, ordinary differential equation (ODE) models are used to model the time and dose dependency of the abundances of molecular compounds as well as interactions and translocations. A…
Authors not listed
Inverse problems, where we seek the values of inputs to a model that lead to a desired set of outputs, are a challenges subset of problems in science and engineering. In this work we demonstrate the use of two generative AI methods to solve inverse problems. We compare this approach to two more conventional approaches…
Authors not listed
Deriving versatile and robust mechanistic models from experimental data is a key challenge in engineering and natural sciences. This is especially true in chemical reaction engineering, where reactor manufacturers and operators increasingly pursue the development and maintenance of digital twins that rely on frequent…
Jane Kondev, Marc Kirschner, Hernan G. Garcia, Gabriel L. Salmon + 1 more
Many biological processes can be thought of as the result of an underlying dynamics in which the system repeatedly undergoes distinct and abortive trajectories with the dynamical process only ending when some specific process, purpose, structure or function is achieved. A classic example is the way in which…