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math.NA2024
A finite difference method with symmetry properties for the high-dimensional Bratu equation
Muhammad Luthfi Shahab, Hadi Susanto, Haralampos Hatzikirou
Solving the three-dimensional (3D) Bratu equation is highly challenging due to the presence of multiple and sharp solutions. Research on this equation began in the late 1990s, but…
math.NA2024
Neural networks for bifurcation and linear stability analysis of steady states in partial differential equations
Muhammad Luthfi Shahab, Hadi Susanto
This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength…