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math.NA2025
Multi-Scale Finite Expression Method for PDEs with Oscillatory Solutions on Complex Domains
Gareth Hardwick, Haizhao Yang
Solving partial differential equations (PDEs) with highly oscillatory solutions on complex domains remains a challenging and important problem. High-frequency oscillations and intr…
math.NA2024
Solving High-Dimensional Partial Integral Differential Equations: The Finite Expression Method
Gareth Hardwick, Senwei Liang, Haizhao Yang
In this paper, we introduce a new finite expression method (FEX) to solve high-dimensional partial integro-differential equations (PIDEs). This approach builds upon the original FE…