Electronic Research Archive (Apr 2023)
Barycentric rational interpolation method for solving fractional cable equation
Abstract
A fractional cable (FC) equation is solved by the barycentric rational interpolation method (BRIM). As the fractional derivative is a nonlocal operator, we develop a spectral method to solve the FC equation to get the coefficient matrix as the full matrix. First, the fractional derivative of the FC equation is changed to a nonsingular integral from the singular kernel to the density function. Second, an efficient quadrature of a new Gauss formula is constructed to compute it simply. Third, a matrix equation of the discrete FC equation is obtained by the unknown function replaced by a barycentric rational interpolation basis function. Then, convergence rate for FC equation of the BRIM is derived. At last, a numerical example is given to illustrate our results.
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