An Extension of the Legendre-Galerkin Method for Solving Sixth-Order Differential Equations with Variable Polynomial Coefficients

Algorithm 1

Compute the matrices {𝑍^𝜇_𝑗,𝑍^𝜈_𝑗for=0,1,2,3}, {𝑍^𝜌_𝑗,𝑍^𝜎_𝑗for𝑗=0,1,2} and {𝑍^𝛿₀,𝑍^𝜀₀}

from Theorem 2.2.

Find the tensor product of the matrices in the previous step.

Compute 𝐹 and write it in a column vector 𝐟.

Obtain a column vector 𝐯 by solving (3.9).