Differential Equations and Inverse Problems, 2nd Edition
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".
Deadline for manuscript submissions: 30 October 2025 | Viewed by 2865
Special Issue Editors
Interests: deep learning; reinforcement learning; multiscale methods (multigrid and wavelet); homotopy method; inverse and Ill-posed problems; parameter reconstruction
Special Issues, Collections and Topics in MDPI journals
Interests: structure-preserving algorithms for differential equations; numerical methods for stochastic differential equation
Special Issues, Collections and Topics in MDPI journals
Interests: computational finance; iterative methods; computational mathematics; stochastic differential equations
Special Issues, Collections and Topics in MDPI journals
Special Issue Information
Dear Colleagues,
This Special Issue builds upon our previous Special Issue, “Differential Equations and Inverse Problems”. Differential equations and inverse problems have become a rapidly growing topic because of recent new techniques and amazing achievements in computational sciences. With the progress of science and technology, differential equations and inverse problems have quickly developed, and new waves have been successively set off in a broad range of disciplines, such as mathematics, physics, engineering, business, economics, earth science, and biology.
The purpose of this Special Issue is to gather contributions from experts on the theory and numerical aspects of differential equations and inverse problems, including, but not limited to, differential equations and fractional differential equations, initial value problems and related inverse problems, boundary value problems and related inverse problems, inverse problems in imaging, image reconstruction in tomography, stability analysis, regularization methods, novel numerical algorithms (such as multigrid methods, wavelet methods, homotopy methods, and structure-preserving methods), and artificial intelligence (such as deep learning and reinforcement learning). Moreover, we encourage submissions of their applications in various practical areas.
Dr. Tao Liu
Dr. Qiang Ma
Dr. Fazlollah Soleymani
Prof. Dr. Lifeng Guo
Guest Editors
Manuscript Submission Information
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Keywords
- partial differential equations
- ordinary differential equations
- stochastic differential equations
- fractional differential equations
- fractional calculus
- inverse and ill-posed problems
- imaging
- image reconstruction
- tomography
- tomographic reconstruction
- regularization methods
- numerical methods
- structure-preserving methods
- minimax methods
- artificial intelligence
- deep learning
- reinforcement learning
- compact radial basis function approximations
- approximations based on neural networks
- node layouts for irregular domains
- multi-asset option pricing problems
- numerical methods for matrix functions
- iterative methods for the solution of nonlinear equations
- Schulz-type iterative method for generalized matrix inversion
- biostatistics and pattern recognition
- combination counting
- separation theory
- information security
- existence of solutions
- exact solutions
- fractional Fourier transform and its applications
- interdisciplinary application of mathematics and other disciplines
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Related Special Issue
- Differential Equations and Inverse Problems in Axioms (12 articles)
