Pantograph equations are fundamental models of delay differential equations that are used to model a variety of physical and engineering phenomena. This manuscript presents a numerical scheme using Chebyshev collocation for solving general pantograph equations with variable coefficients and linear functional arguments. Nonlinear pantograph differential equations are transformed into nonlinear algebraic equations which provide matrix representations. A numerical algorithm is used to solve nonlinear algebraic equations in their unknowns. Using residual functions, we developed a method for analyzing errors in the proposed scheme. It is shown that the proposed method is accurate and effective for Pantograph equations. We provide numerical examples of linear and nonlinear problems to confirm the effectiveness and reliability of the proposed method.

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Chebyshev Collocation Method for Pantograph Delay Differential Equations with Linear Functional Arguments

  • Fathalla A. Rihan,
  • Ola Mohamed

摘要

Pantograph equations are fundamental models of delay differential equations that are used to model a variety of physical and engineering phenomena. This manuscript presents a numerical scheme using Chebyshev collocation for solving general pantograph equations with variable coefficients and linear functional arguments. Nonlinear pantograph differential equations are transformed into nonlinear algebraic equations which provide matrix representations. A numerical algorithm is used to solve nonlinear algebraic equations in their unknowns. Using residual functions, we developed a method for analyzing errors in the proposed scheme. It is shown that the proposed method is accurate and effective for Pantograph equations. We provide numerical examples of linear and nonlinear problems to confirm the effectiveness and reliability of the proposed method.