Efficient solving of partial differential equations with new numerical methods

Yadav, Ravi; Wani, Tanveer Ahmad; Mokashi, Mandar K.; Navale, Shirish Jaysing; Khudaynazarov, Egambergan; Khidse, Swati V.

doi:10.47974/JIM-2493

Open Access Research Article

Efficient solving of partial differential equations with new numerical methods

Ravi Yadavravi.yadav@symlaw.ac.inSymbiosis Law School Pune (SLS-P)Symbiosis Centre for Advanced Legal Studies and Research (SCALSAR), Symbiosis International (Deemed University)Pune, Maharashtra, 411014, IndiaView full profile → , Tanveer Ahmad Wanitanveer.ahmad@niu.edu.inDepartment of PhysicsNoida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , ^*Mandar K. MokashiCorresponding authormandar.mokashi16@gmail.comDepartment of Computer Science and Engineering (Artificial Intelligence & Analytics)School of ComputingMIT-ADT UniversityPune, Maharashtra, 412201, IndiaView full profile → , Shirish Jaysing Navalesjnavale@aissmscoe.comDepartment of Mechanical EngineeringAISSMS College of EngineeringPune, Maharashtra, 411001, IndiaView full profile → , Egambergan Khudaynazarove.xudaynazarov@mamunedu.uzDepartment of General Professional SciencesMamun UniversityKhiva, 220900, Uzbekistan0009-0000-1210-8113View full profile → , Swati V. Khidseswatikhidse@gmail.comDepartment of Computer Science and EngineeringCSMSS Chh. Shahu College of EngineeringAurangabad, Maharashtra, 431001, IndiaView full profile →

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pp. 587–596Vol. 29Issue 3March 2026DOI: 10.47974/JIM-2493XML

Received:: 01 Apr 2025
Published Online:: 18 Mar 2026
Article type:: Research Article
Language:: EN
Article no.:: JIM-2493
Pages:: 587–596

Abstract

Partial Differential Equations (PDEs) play a very significant role in the life of scientists and engineers who wish to model complex physical processes. However, standard solutions to math have a hard time striking the correct balance of accuracy, stability, and the speed at which they can be of their tasks. In this research, it is proposed that new numeric techniques can be used to solve PDEs at a fast rate, higher convergence rates and reduced costs of computing. The new techniques utilise a better summability and flexible discretisation to provide a large variety of border cases and nonlinearities. Most computer experiments demonstrate that the proposed methods are faster and more precise compared to alternative approaches to the standard PDE problems. It is now possible to have fluid dynamics, heat movement, and electromagnetism models that are more precise. The study demonstrates that big computer systems may be able to use scalable application.

Keywords

Partial differential equations Numerical methods Adaptive discretization Summability techniques Computational efficiency

Subject Classifications

32W5033F05

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