Differential Equations and Inverse Problems
A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".
Deadline for manuscript submissions: closed (28 August 2024) | Viewed by 12545
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: ill-posed problems; regularization method; inverse source problems; backward problems; parabolic equation; elliptic equation; fractional diffusion equation; convergence analysis
Special Issue Information
Dear Colleagues,
Differential equations and inverse problems have become a rapidly growing topic because of the new techniques developed recently 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, biology, etc.
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, structure-preserving methods), and artificial intelligence (such as deep learning, reinforcement learning). Moreover, we encourage submissions of their applications in various practical areas.
Dr. Tao Liu
Dr. Qiang Ma
Dr. Songshu Liu
Guest Editors
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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
- artificial intelligence
- deep learning
- reinforcement learning
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