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**Fourier operational matrices of differentiation and transmission: introduction and applications.**
*(English)*
Zbl 1275.65036

Summary: This paper introduces Fourier operational matrices of differentiation and transmission for solving high-order linear differential and difference equations with constant coefficients. Moreover, we extend our methods for generalized pantograph equations with variable coefficients by using Legendre Gauss collocation nodes. In the case of numerical solutions of pantograph equation, an error problem is constructed by means of the residual function and this error problem is solved by using the mentioned collocation scheme. When the exact solution of the problem is not known, the absolute errors can be computed approximately by the numerical solution of the error problem. The reliability and efficiency of the presented approaches are demonstrated by several numerical examples, and also the results are compared with different methods.

### MSC:

65L03 | Numerical methods for functional-differential equations |

34K28 | Numerical approximation of solutions of functional-differential equations (MSC2010) |

65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |

### Keywords:

error bounds; Fourier operational matrices; pantograph equations; Legendre Gauss collocation; numerical examples
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\textit{F. Toutounian} et al., Abstr. Appl. Anal. 2013, Article ID 198926, 11 p. (2013; Zbl 1275.65036)

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