### Approximate Solution of Multi-Pantograph Equations With Variable Coefficients via Collocation Method Based on Hermite Polynomials

Dianchen Lu, Chen Yuan, Rabia Mehdi, Shamoona Jabeen, Abdur Rashid

#### Abstract

This research article presents an approximate solution of the non-homogenous Multi-Pantograph equation comprising of variable coefficients by utilizing a collocation method based on Hermite polynomials. These orthogonal polynomials along with its collocation points transform the equation and the initial conditions into matrix equation comprising of a system of linear algebraic equations. Subsequently, by solving this system, the unknown Hermite coefficients are calculated. To reveal the accuracy and efficiency of the method applied, the approximate results obtained by this technique have been compared with exact solutions. Moreover, some numerical illustrations in the form of examples are given to exhibit the applicability of the proposed technique.

#### Keywords

Multi-Pantograph equation; Collocation method; Hermite polynomials; Matrix equation; Approximate results; Accuracy

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DOI: http://dx.doi.org/10.26713%2Fcma.v9i4.844

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