Pell Collocation Pseudo Spectral Scheme for One-Dimensional Time-Fractional Convection Equation with Error Analysis

Algorithm 1

Coding algorithm for the proposed scheme.

 Input; the functions and .

 Step 1. Define Pell polynomials by (9).

 Step 2. Compute the basis function of Pell polynomials by (29).

 Step 3. Define the basis function vector by (28).

 Step 4. Substituting Eqs. (2) and (26) into Eq. (1).

 Step 5. Collocating Eq. (32) in roots of the polynomial .

 Step 6. Compute the matrix using (35).

 Step 7. Define the unknown vectors .

 Step 8. Use command to solve the system .

 Output The approximate solution: .