Quantum mechanics

Pure mathematics

Differential equation

Applied mathematics

Computer science

Legendre wavelet

Collocation method

Wavelet transform

Spectral method

Algebraic equation

Discrete wavelet transform

Physics

Nonlinear system

Kernel (algebra)

Collocation (remote sensing)

Mathematics

Legendre polynomials

Mathematical analysis

Artificial intelligence

Ordinary differential equation

Fractional calculus

Machine learning

Wavelet

Chinese Journal of Physics

In the recent years, few type of fractional derivatives which have non-local and non-singular kernel are introduced. In this work, we present fractional rheological models and Newell-Whitehead-Segel equations with non-local and non-singular kernel. For solving these equations, we present a spectral collocation method based on the shifted Legendre polynomials. To do this, we extend the unknown functions and its derivatives using the shifted Legendre basis. These expansions and the properties of the shifted Legendre polynomials along with the spectral collocation method will help us to reduce the main problem to a set of nonlinear algebraic equations. Finally, The accuracy and efficiency of the proposed method are reported by some illustrative examples.

A numerical study of fractional rheological models and fractional Newell-Whitehead-Segel equation with non-local and non-singular kernel