9 papers · ranked by Valyu relevance
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…
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…
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…
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…
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…
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…
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…