In this paper, a new and efficient approach based on the generalized Laguerre matrix method for numerical approximation of the linear differential-difference equations (DDEs) with variable coefficients is introduced. Explicit formulae which express the generalized Laguerre expansion coefficients for the moments of the derivatives of any differentiable function in terms of the original expansion coefficients of the function itself are given in the matrix form. In the scheme, by using this approach we reduce solving the linear differential equations to solving a system of linear algebraic equations, thus greatly simplify the problem. In addition, several numerical experiments are given to demonstrate the validity and applicability of the method.
Bojdi, Z. K.; Ahmadi-Asl, S.; and Aminataei, A.
The Generalized Laguerre Matrix Method or Solving Linear Differential-Difference Equations with Variable Coefficients,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 9,
1, Article 17.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss1/17