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A new method for solving non‐autonomous ordinary differential equations is proposed, the method achieves spectral accuracy. It is based on a new result which expresses the solution of such ODEs as an element in the so called ⋆‐algebra. This algebra is equipped with a product, the ⋆‐product, which is the integral over the usual product of two bivariate distributions. Expanding the bivariate distributions...
The solution of systems of non‐autonomous linear ordinary differential equations is crucial in a variety of applications, such us nuclear magnetic resonance spectroscopy. A new method with spectral accuracy has been recently introduced in the scalar case. The method is based on a product that generalizes the convolution. In this work, we show that it is possible to extend the method to solve systems...
We present different sampling methods for the approximation of functions on the sphere. In this note we focus on Fourier methods on the sphere based on spherical harmonics and on the double Fourier sphere method. Further longitude-latitude transformation is combined with Fourier extension to allow the use of bi-periodic Fourier series on the sphere. Fourier extension with hermite interpolation is...
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