Linear barycentric rational collocation method for solving telegraph equation

Abstract

In this paper, the linear barycentric rational interpolation collocation method for solving one‐ and two‐dimensional telegraph equation is presented. The barycentric rational interpolation is introduced. Following the barycentric rational interpolation method, the matrix form of the collocation method is also obtained which can be easily programmed. With the help of the convergence rate of the linear barycentric rational interpolation, the convergence rate of linear barycentric rational collocation method for solving telegraph equation is proved. At last, several numerical examples are provided to show the convergence rate and verify the correctness of the theoretical analysis.

Solving Nonlinear Wave Equations Based on Barycentric Lagrange Interpolation

“…The barycentric Lagrange interpolation method and Crank-Nicolson scheme are combined to solve the two-dimensional Allen-Cahn equation [26]. In addition, the barycentric Lagrange interpolation method was used to solve telegraph equation [27], heat conduction equation [28], beam vibration equation [29], and so on.…”

Barycentric Rational Collocation Method for Nonlinear Heat Conduction Equation

“…Floater and Kai, Klein and Berrut [15][16][17] have proposed a rational interpolation scheme and get the equidistant node of the barycentric formula. In recent papers, references [18][19][20][21][22][23][24][25] have been extended the barycentric collocation methods to solve initial/boudary value problems and linear/nonlinear problems.…”