Two spectral Gegenbauer methods for solving linear and nonlinear time fractional Cable problems

Abstract

This research aims to analyze and implement two numerical spectral schemes for solving linear and nonlinear time fractional Cable equations (TFCEs). Two modified sets of shifted Gegenbauer polynomials (SGPs) are used as basis functions. The approximation of the solution is written as a product of the two chosen basis function sets. For these methods, the principle idea is to convert the problem governed by the underlying conditions into a set of linear and nonlinear algebraic equations that can be solved using appropriate numerical techniques. The upper estimate of the truncation error for the proposed expansion is investigated. In the end, four examples are presented to illustrate the accuracy of the suggested schemes.