Abstract

The method of Chebyshev polynomials is introduced to represent approximate solutions of first‐order partial differential equations consisting of two independent variables. A set of linear algebraic equations is obtained by using the properties of Chebyshev polynomials and Kronecker product to analyse first‐order partial differential equations. The coefficient vector of Chebyshev polynomials of the first‐order partial differential equations can be obtained directly from Kronecker product formulas, which are suitable for computer computation. A numerical example for a set of first‐order partial differential equations is solved by a Chebyshev polynomials approximation and the results are satisfactory.