AI & ML
A Christov Integrating Factor Method for Approximating Rational PDE Solutions
arXiv cs.NA0 views
arXiv:2611.07154v1 Announce Type: cross Abstract: Rational solutions of partial differential equations (PDEs) are notoriously difficult to approximate via spectral Fourier methods due to their algebraically slow decay rate. In this work we discuss approximating rational PDE solutions in a basis of orthogonal functions known as the Christov functions, allowing for the computation of its spectrum via the fast Fourier transform. An explicit fourth-order integrating factor method is derived. The effectiveness of the method is tested on several nonlinear PDEs. Relative to a straightforward pseudo-spectral approximation, the integrating factor method supports larger regions of stability resulting in a more efficient scheme.
Source：https://arxiv.org/abs/2611.07154PreviousImproving the accuracy of the momentum-exchange method in lattice Boltzmann methodsNextContinuous Space-Time Finite Element Simulations for Biomedical Flows with Large Boundary Motion and Time-Periodicity
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