Comparative study of Fourier transform and an approach of fast Fourier transform in solving the boundary value problem of PDEPartial differential equationdiscrete fourier transformfast fourier transformfast fourier fitThe article compares Fast Fourier Transform (FFT) against the Fourier Transform in solving...
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We solved the PDEinline_formula not implementedby transforming our functions into vectors of numbersinline_formula not implementedandinline_formula not implemented, transforming second derivative into a linear operator (a matrix)inline_formula not implemented, and solvinginline_formula not implementedusing ba...
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Chladni Figures and the Tacoma Bridge: Motivating PDE Eigenvalue Problems via Vibrating Plates Teaching linear algebra routines for computing eigenvalues of a matrix can be well motivated for students by using interesting examples. We propose in this... MJ Gander,F Kwok - 《Siam Review》 被引量...
Using neural networks to approximate the function : These algorithms are suitable for a PDE with a fixed differential operator and the right-hand side . The most notable advantage of this approach is that they can: 1) overcome the curse of dimensionality and solve high-dimension PDEs; 2) reso...
. But one can check using algebra that if , then , and similarly with the inequalities reversed; this allows the argument as stated to be made rigorous. (One can also argue by considering the rectangle with the narrowest side, and showing that it is adjacent to one which is even narrower...
Experiments show that such a c does produce a very good numerical solution to the PDE, even if the value of c is not exactly the experimentally optimal one. If one insists on finding the experimentally optimal value, it can be achieved by a moderate search. The stopping criterion is ...
In this work, we generated experimental data for the SQG equation, using the Fourier pseudospectral method, and for the Gray–Scott equation, using the finite difference method. Our study demonstrated the accuracy of the FNO in solving complex nonlinear PDE problems, and it achieved a relative er...
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