https://ijesar.in/index.php/ijesar/issue/feed 2026-05-29T04:58:59+00:00 IJESAR-PUBLISHER innovativelibrary6@gmail.com Open Journal Systems <p style="text-align: justify;">&nbsp;</p> <p style="text-align: justify;"><span style="font-family: lucida sans unicode,lucida grande,sans-serif;"><span style="font-size: 14px;"><strong>International Journal of Engineering Science and Generic Research (IJESAR) is a full-text database of OJS journal</strong></span></span></p> <p style="text-align: justify;"><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">IJESAR is International publisher of academic and research journals; IJESAR publishes and develops titles in groups with the world's most prestigious learned societies and publishers. Our goal is to bring high quality research work</span></p> <p style="text-align: justify;"><span style="font-family: lucida sans unicode,lucida grande,sans-serif;"><span style="font-size: 14px;"><strong>Aims and Scope&nbsp;&nbsp;</strong></span></span></p> <p style="text-align: justify;"><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">International&nbsp;Journal of Engineering Science and Generic Research&nbsp;(IJESAR) is an&nbsp;Open Access, international, multidisciplinary journals hub in the field multi disciplinary&nbsp;and will publish original research papers, short communications, invited reviews, Case studies and editorial commentary and news, Opinions &amp; Perspectives and Book Reviews written at the invitation of the Editor in following fields</span></p> <p style="text-align: justify;"><span style="font-family: lucida sans unicode,lucida grande,sans-serif;"><span style="font-size: 14px;"><strong>Important Notice&nbsp;&nbsp;</strong></span></span></p> <p style="text-align: justify;"><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">Authors can now directly send their manuscript as an email attachment to editor@ijesar.in&nbsp;</span></p> <p style="text-align: justify;"><span style="font-family: lucida sans unicode,lucida grande,sans-serif;">All manuscripts are subject to rapid peer review. Those of high quality (not previously published and not under consideration for publication in another journal) will be published without delay. First-time users are required to register themselves as an author before making submissions by signing up the author registration form at journals website:&nbsp;</span><span style="font-size: 14px; font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">www. http://ijesar.in</span></p> <p style="text-align: justify;"><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">With the online journal management system that we are using, authors will be able to track manuscripts progress through the editorial process by logging in as author in authors Dashboard.</span></p> <p style="text-align: justify;"><span style="font-family: lucida sans unicode,lucida grande,sans-serif;"><span style="font-size: 14px;"><strong>Top Reasons for publication with us</strong></span></span></p> <p style="text-align: justify;"><strong style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">Quick Quality Review:</strong><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">&nbsp;The journal has strong international team of editors and reviewers, Rapid Decision and Publication</span></p> <p style="text-align: justify;"><strong style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">Very Low Publication Fees:</strong><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">&nbsp;Comparable journals charge a huge sum for each accepted manuscript. IJESAR only charge the fees necessary to recoup cost associated with running the journal</span></p> <p style="text-align: justify;"><strong style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">Other features:</strong><span style="font-family: 'lucida sans unicode', 'lucida grande', sans-serif;">&nbsp;DIDS Assigned and Implemented the Open Review System (ORS).</span></p> https://ijesar.in/index.php/ijesar/article/view/260 2026-05-29T04:58:59+00:00 Soniya Mittal sohniyamittal@gmail.com Vishal Saxena editor@ijesar.in

<p style="font-weight: 400;">In this paper, we systematically review the literature on numerical methods for solving differential equations, integral equations and integro-differential equations. This paper investigates classical numerical techniques, including finite difference methods, finite element methods, spectral methods, collocation methods, and wavelet-based approaches, emphasising the mathematical fundamentals, the convergence behaviour, and computational efficiency. Modern developments, especially on spectral collocation methods, wavelet approaches, fractional calculus techniques and adaptive numeric schemes for boundary value and fractional-order problems are emphasized.</p> <p style="font-weight: 400;">It also explores new machine learning–based methods, especially Physics-Informed Neural Networks (PINNs), Deep Operator Networks, and hybrid computational methods that merge numerical analysis with artificial intelligence. The resulting methods have received much attention since they show better flexibility, faster computation, and more powerful for solving high-dimensional and nonlinear partial differential equations. It also covers recent progress on tensor-network methods and quantum-enhanced PINNs, before moving to require more involved scientific and engineering applications and discussing quantum-enhanced methods based on stochastic differential equation solvers.</p> <p style="font-weight: 400;">This study further discusses the advantages and disadvantages of the different numerical methods based on the accuracy, convergence process, stability, computational complexity, and suggestions for applications to real problems. This review suggests that the computational mathematics of the future is at an exciting juncture as it increasingly shifts towards the use of hybrid and adaptive frameworks combining classical numerical methods with machine learning techniques targeted to efficiently solving large-scale, multi-physics and data-driven problems. Numerical solution of equations arising in science and engineering: Outlook and directions AbstractThis paper provides an informative guide to what is happening now and what is expected to happen in the field of numerical solutions of mathematical equations in the future.</p> <p style="font-weight: 400;"><strong>Keywords:</strong> Numerical Methods, Differential Equations,Spectral Collocation Methods, Finite Element Method (FEM), Integro-Differential Equations, Physics-Informed Neural Networks (PINNs) ,Fractional Calculus</p>

2026-05-29T00:00:00+00:00 Copyright (c) 2026 International Journal of Engineering Science and Generic Research