Approximate Solution Of Multi-pantograph Equations With Variable Coefficients Via Collocation Method Based On Hermite Polynomials

In recent decades,the application of delay differential equations has played an important role in the theoretical research of many applied sciences such as science,engineering,biology and so on.However,there is no unified method for solving delay differential equations.The main reason is that the existence of delay term in the equation brings many difficulties to the solution of delay differential equations.With the application of multi-pantograph delay differential equation more and more widely,scholars pay more and more attention to the field of solving delay differential equation.In this paper,the approximate solutions of non-homogeneous multi-pantograph delay differential equations with variable coefficients are obtained by combining the concepts of Hermite polynomials with the collocation method.Firstly,the orthogonal polynomials and their collocation points are selected to transform the non-homogeneous multi-pantograph delay differential equation with variable coefficients and the initial conditions into matrix equations.Secondly,the unknown Hermite coefficient is calculated by solving the corresponding matrix equation.Then,different nodes are selected and the results obtained by this method are compared with the exact solutions by using mathematical software,which verifies the accuracy and validity of this method.In addition,numerical simulations of some examples are given to illustrate the applicability of the proposed method.