Mathematics

Research Notes on Computing and Communication Sciences

Solving Differential Equations
A Computational Approach

EDITORS: Dr. Geeta Arora
Dr. Firdous A. Shah

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Solving Differential Equations

CALL FOR BOOK CHAPTERS
Pub Date: TBA
Hardback Price: TBA
Hard ISBN: 
Pages: TBA
Binding Type: 
Series: Research Notes on Computing and Communication Sciences

CALL FOR BOOK CHAPTERS

Short Description of the Book:


We are inviting contributions for a new edited book titled Solving Differential Equations: A Computational Approach. This book aims to provide a comprehensive and up-to-date exploration of computational methods for solving ordinary and partial differential equations (ODEs and PDEs).

The book will bridge the gap between theoretical understanding of differential equations and their practical solution using computational techniques. It will be targeted towards students, researchers, and practitioners in science, engineering, and mathematics who rely on solving differential equations in their work.

Coverage:
We welcome submissions on a wide range of topics related to the computational solution of differential equations, including but not limited to:

  • Application of Machine Learning for Solving PDEs
  • Advancement of Classical Methods for Solving ODEs (EG, Runge-Kutta Methods, Multistep Methods)
  • Application of Finite Difference and Finite Element Methods for PDEs
  • Spectral Methods for PDEs
  • Stiff ODE Solvers
  • Numerical and Analytical Approaches to Solve Boundary Value Problems
  • Applications of Computational Methods to Specific Scientific and Engineering Problems
  • Insight on Application of the Eigenvalues in Solving Differential Equations
  • Parallel and High-Performance Computing for Differential Equations
  • Gradient-Based Optimization Methods
  • Leveraging Existing CAD Geometry for Mesh Generation in Finite Element Methods
  • Discontinuous Galerkin Methods for Solving PDEs with Complex Geometries or Discontinuities
  • Analyzing the Stability and Convergence of Explicit Finite Difference Schemes
  • Lax-Richtmyer Stability Criterion: A General Stability Condition for Explicit Time-Marching Schemes for Hyperbolic PDEs
  • Semigroup Methods: Formulating the Evolution of Solutions within a Functional Analysis Framework
  • Variational Formulations: Rewriting PDEs into a Variational Form Suitable for Finite Element Methods
  • Fredholm Theory: Applying Results from Functional Analysis to Analyze Existence and Uniqueness of Solutions for PDEs
  • Preconditioned Conjugate Gradient Methods: Accelerating Krylov Subspace Methods by Preconditioning the System Matrix
  • Multigrid Methods: Solving Systems on a Hierarchy of Coarse and Fine Grids for Improved Efficiency
  • Wavelet Transforms: Understanding the Mathematical Basis of Wavelet-Based Methods for Solving PDEs
  • Fast Fourier Transforms (FTFs): Analyzing the Theoretical Underpinnings of Spectral Methods for PDEs in Periodic Domains
  • Sparse Grid Collocation: Exploring the Mathematical Framework for Solving PDEs with High-Dimensional Parameter Spaces




Important Dates:
Abstract Submission (400 - 600 words):
15th June 2024
Notification of Acceptance: 30 June 2024
Full Chapter (8,000 - 10,000 words) Submission Due: On or before 30th August 2024

Submission procedure:
Researchers and practitioners are invited to submit a one-page chapter proposal or abstract on or before June 5th, 2024, clearly mentioning the title of the paper and author(s) details.
Author(s) will be notified about the status of their proposals by June 15th, 2024.
Full chapters (15-30 pages) are expected to be submitted by August 30th, 2024.
All submitted chapters will be peer-reviewed.

Prospective authors are requested to submit their abstract followed by full-length chapters as an email attachment in a Word file to:
geetadma@gmail.com with CC to fashah79@gmail.com

Authors must refer to the following link for detailed guidelines for chapter preparation: http://www.appleacademicpress.com/publishwithus

Note: There is no publication fee for manuscripts submitted to this book publication. Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere.


About the Authors / Editors:
EDITORS: Dr. Geeta Arora
Professor, Department of Mathematics, Lovely Professional University, Punjab, India. Email: geetadma@gmail.com, geeta.18820@lpu.co.in


Dr. Firdous A. Shah
Associate Professor, Department of Mathematics, University of Kashmir, South Campus, Anantnag-192101, Jammu and Kashmir, India. E-mail: fashah@uok.edu.in; fashah79@gmail.com





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