Polynomial Bases on the Sphere

2002 ◽  
pp. 39-52 ◽  
Author(s):  
Noemí Laín Fernández
Keyword(s):  
Polynomial Bases

scholarly journals A fast sparse spectral method for nonlinear integro-differential Volterra equations with general kernels

2021 ◽  
Vol 47 (3) ◽  
Author(s):  
Timon S. Gutleb
Keyword(s):  
Open Source ◽  
Spectral Method ◽  
Jacobi Polynomial ◽  
Numerical Experiments ◽  
Exponential Convergence ◽  
Analytic Solutions ◽  
Convolution Type ◽  
Volterra Equations ◽  
Polynomial Bases ◽  
Sparsity Structure

AbstractWe present a sparse spectral method for nonlinear integro-differential Volterra equations based on the Volterra operator’s banded sparsity structure when acting on specific Jacobi polynomial bases. The method is not restricted to convolution-type kernels of the form K(x, y) = K(x − y) but instead works for general kernels at competitive speeds and with exponential convergence. We provide various numerical experiments based on an open-source implementation for problems with and without known analytic solutions and comparisons with other methods.

Linearization of matrix polynomials expressed in polynomial bases

2008 ◽  
Vol 29 (1) ◽  
pp. 141-157 ◽  
Author(s):  
A. Amiraslani ◽  
R. M. Corless ◽  
P. Lancaster
Keyword(s):  
Matrix Polynomials ◽  
Polynomial Bases
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