Numerical Methods for Differential Equations and Related Inverse Problems
A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "C1: Difference and Differential Equations".
Deadline for manuscript submissions: 30 April 2026 | Viewed by 755
Special Issue Editor
Interests: numerical methods of partial differential equations and fractional differential equations; computational methods and numerical analysis related to plasma physics and magnetohydrodynamics; machine learning and deep learning methods; medical imaging; inverse problems
Special Issue Information
Dear Colleagues,
We are pleased to announce that the Special Issue entitled "Numerical Methods for Differential Equations and Related Inverse Problems" is now open for submissions. The Issue aims to encompass a wide range of topics involving numerical methods for partial differential equations (PDEs), fractional differential equations (FDEs), and integro-differential equations.
We particularly encourage submissions featuring novel algorithms or applications based on mesh-based methods, including finite difference, finite volume, finite element, discontinuous Galerkin and spectral methods. Additionally, contributions exploring the development of meshfree methods, such as smooth-particle hydrodynamics, partition of unity methods, and the method of particular solutions, are welcomed.
In light of the rapid advancements in machine learning and artificial intelligence algorithms and their diverse applications, we are especially interested in papers that apply these methods to solve various differential equations models. Submissions that offer novel insights into machine-learning-based PDE and FDE solvers are highly encouraged.
Furthermore, this Special Issue also seeks excellent papers on numerical methods for solving inverse problems related to differential equations. Our goal for this Special Issue is to serve as an active forum where researchers worldwide can exchange ideas and advance our understanding of numerical methods for differential equations and related inverse problems, thereby inspiring more innovative work in these fields.
Dr. He Yang
Guest Editor
Manuscript Submission Information
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Keywords
- finite difference methods
- finite element methods
- discontinuous Galerkin methods
- meshfree methods
- method of particular solutions
- partial differential equations
- fractional differential equations
- integro-differential equations
- machine learning-based PDE solver
- inverse problems
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