Solving singularity structures in nonlinear ordinary and partial differential equations
Author(s): Eshwari and Dr. Raj Kumar
Abstract: The study explores various mathematical tools, such as transform methods, integral equations, and regularization techniques, to characterize and resolve singular behavior in PDEs. Emphasis is placed on developing robust numerical algorithms capable of accurately capturing and resolving singularities in complex PDE systems. Furthermore, the thesis addresses the application of singularity analysis in interdisciplinary domains including nonlinear optics, fluid dynamics, and mathematical biology. Case studies illustrate the practical relevance of the proposed methodologies in modeling physical phenomena characterized by singular behavior, shedding light on the underlying mechanisms and offering insights for engineering design and scientific inquiry. Overall, this thesis contributes to advancing the understanding and treatment of singularity structures in nonlinear ODEs and PDEs, offering valuable insights into the nature of singularities and providing effective computational tools for tackling challenging problems across various domains of science and engineering.
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