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Differential Equations

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Differential Equations

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Research Frontiers in Spectral Methods High-Dimensional PDEs

Development and analysis of spectral and pseudospectral numerical schemes for solving high-dimensional partial differential equations.

Curse of Dimensionality in Spectral Approximation Theory
Fourier-Based Methods for Singular Nonlinear PDEs
Exponential Convergence in Unbounded Domain Spectral Problems
Oscillatory Integrals and High-Frequency Wave Propagation
Sparse Spectral Representations of Multiscale Phenomena
Adaptive Basis Selection for Parameter-Dependent PDE Systems
Domain Decomposition with Spectral Element Boundary Coupling
Tensor Methods in Ultra-High Dimensional Elliptic Equations
Spectral Stability Analysis of Stiff Multiphysics Couplings
Reduced Order Models from Spectral Modal Truncation

All Differential Equations PhD categories