Abstract : Nonlinear equations and systems of equations are commonly used to describe scientific and engineering challenges. There are more and more applications for these systems, and majority of the techniques, now in use, have limitations and drawbacks. Thus, it is crucial to create novel numerical techniques that are exceptionally accurate, stable, and reliable. This symposium focuses on the contemporary design methodologies, including machine learning algorithms, conformable fractional equations, and others, to real-world problems such as metabolic pathways, drug delivery interaction problem, image segmentation etc. We bring researchers from a broad spectrum to discuss development and applications of these modern methods.
Organizer(s) : Fiza Zafar, Alicia Cordero, Juan Ramon Torregrosa and Norma Binti Alias
[03387] Efficient iterative scheme for system of nonlinear equations
Format : Online Talk on Zoom
Author(s) :
Himani Arora (Guru Nanak Dev University, Amritsar)
Abstract : Solving systems of nonlinear equations is an important and interesting task in science and engineering. But finding a solution of these systems using analytical methods is almost impossible, so one has to rely on iterative techniques for solution of such problems. The main motive of this talk is to discuss an efficient iterative technique for solving systems of nonlinear equations. The most time consuming and hard task while designing an iterative scheme is the evaluation of the inverse of the derivative. The main feature of the scheme presented is that it only utilizes one inverse evaluation per iteration, which makes the scheme computationally efficient. The efficiency of the scheme is verified through a number of real-world problems like integral equations and boundary value problems etc.
[03352] Analysis of Love-type wave in a nonlocal piezoelectric composite
Format : Talk at Waseda University
Author(s) :
Vanita Sharma (SVKM's NMIMS Chandigarh)
Abstract : The aim of this research article is to provide a more detailed investigation of the size influences in piezoelectric material subjected to Love-type wave propagation. With the goal to consider the size influences of the structure, the Eringen's nonlocal theory is utilized. The dispersion relations for piezoelectric composite are obtained. Thereafter, detailed investigations of various affecting parameters viz. nonlocal parameter, material parameters etc. on the wave dispersion characteristics of size-dependent nanoscaled structure are addressed.
[03084] Non-Linear GAC Model for GIS Image Segmentation of Deforestation in Nusajaya Malaysia
Format : Online Talk on Zoom
Author(s) :
norma binti alias (universiti teknologi malaysia)
fiza zafar (Bahauddin Zakariya University)
Abstract : Based on the statistical data from website Global Forest Watch, from year 2001 to 2021, Nusajaya , Johor Malaysia experience a loss of 745kha of tree cover which is equivalent to a 47% decrease and a 292Mt of increase in CO2 emissions . GIS images able to visualize the deforestation problem. Digital transformation of images can be analysed by non-linear GAC Model for image segmentation. Numerical performance evaluation obtained the validation and verification of the analysis.
[03396] Mathematical modelling of Wave Equation in Elastodynamics Problems
Format : Online Talk on Zoom
Author(s) :
Maryam Abdullah Alharbi (UTM)
Norma binti Alias (UTM)
Abstract : The study of the wave equation in elastodynamics is crucial for understanding various physical phenomena. We present a mathematical model that describes the behavior of waves in elastodynamics. The model is stable to solve using FDM, which means this model is convergent to the approximate solution. Additionally, we highlight the relationship between blood flow and elastodynamics. We discuss the behavior of blood vessels and their interaction with blood as a fluid.
[03928] Iterative Newton type methods with fractional derivatives
Format : Online Talk on Zoom
Author(s) :
Juan R. Torregrosa (Universitat Politècnica de València)
Alicia Cordero (Universitat Politècnica de València)
Paula Triguero Navarro (Universitat Politècnica de València)
Abstract : Recently, several iterative methods using fractional derivatives have been designed. In this work, we propose some iterative schemes with fractal and conformable derivatives for solving nonlinear equations $f(x)=0$. We analyze the local convergence of these algorithms and study their stability and computational performance. This stability is compared with those of iterative procedures using standard derivatives.
[03702] A Hybrid Genetic Algorithm for Solving Nonlinear Systems and Applications
Nabeera Ahmad Gillani (CASPAM, Bahauddin Zakariya University, Pakistan)
Abstract : In this talk, a hybrid genetic algorithm has been proposed to solve nonlinear systems of equations by combining genetic algorithm and a fourth order convergent Jarratt type method to guarantee convergence and to accelerate the process of obtaining the solution. The proposed method is then applied to optimize biochemical systems to maximize the production and minimize the reaction’s concentration. The performance and computational time of genetic algorithm and hybrid genetic algorithm have also been analyzed.
[03357] Iterative Method for Efficiently Computing Generalized Inverses of Matrices
Format : Talk at Waseda University
Author(s) :
MANPREET KAUR (Lovely Professional University)
Abstract : The study of generalized inverses of matrices has been extensively explored in recent years. An iterative approach for finding the Moore-Penrose inverse of a matrix is discussed. The method’s convergence is analyzed, achieving fourth-order convergence under certain conditions, with a suggested parameter choice for improved convergence order. Testing on real-life matrices from the Matrix-Market Library shows the proposed scheme’s superiority over existing methods. The study also investigates the most efficient parameter choice.
[03376] Globally convergent iterative method for evaluating matrix sign function
Format : Talk at Waseda University
Author(s) :
Munish Kansal (Thapar Institute of Engineering and Technology, Patiala, Punjab 147004)
Abstract : The matrix sign function plays a vital role in the various fields of scientific computing. This work proposes an iterative method to compute the matrix sign function of a matrix having no eigenvalues on the imaginary axis and is analyzed for convergence and asymptotic stability. Global convergence behavior is provided by drawing basins of attraction. Numerical experiments of different dimensions support the theoretical results and illustrate the efficiency of the proposed method.
02411 (3/3) : 4E @E604 [Chair: Juan Ramon Torregrosa]
[03040] An Iterative scheme for finding simultaneous roots of nonlinear systems
Format : Talk at Waseda University
Author(s) :
Neus Garrido (Universitat Politècnica de València)
Paula Triguero Navarro (Universitat Politècnica de València)
Alicia Cordero (Universitat Politècnica de València)
Juan Ramón Torregrosa (Universitat Politècnica de València)
Abstract : Systems of nonlinear equations usually appear in many real-world applications. We give a general iterative algorithm to approximate simultaneous solutions of systems of nonlinear equations. We show that by adding a general sub-step to any iterative method, a new iterative scheme to approximate simultaneous roots of nonlinear systems with doubled convergence order can be obtained. We add this sub-step to some iterative methods of this domain and analyze the behavior of the new schemes.
[03925] High-order iterative methods for solving nonlinear systems
Format : Online Talk on Zoom
Author(s) :
Alicia Cordero
Renso V. Rojas-Hiciano (Pontificia Universidad Católica Madre y Maestra)
Juan R. Torregrosa (Universitat Politècnica de València)
Abstract : In the last decades, many optimal iterative schemes have been developed for solving nonlinear equations, for simple or multiple roots. However, the amount of vectorial iterative procedures able to estimate the solutions of nonlinear systems could be higher. The computational cost of solving the linear systems involved in each iteration plays a key role in the design, seeking the efficiency of the method. We present a highly efficient scheme for solving nonlinear systems of equations.
