A steady barycentric Lagrange interpolation method for the 2D higher‐order time‐fractional telegraph equation with nonlocal boundary condition with error analysis

Abstract

In this paper, we consider the numerical solution of the time‐fractional telegraph equation with a nonlocal boundary condition. A novel barycentric Lagrange interpolation collocation method is developed to solve this equation. Two difficulties have been sorted: the singularity of the integration and the higher accuracy. At the same, we put forward a steady barycentric Lagrange interpolation technique to overcome the new “Runge” phenomenon in computation. Error estimates of the barycentric Lagrange interpolation and the time‐fractional telegraph system for the present method are presented in Sobolev spaces. High convergence rates of the proposed method are obtained and are consisted with the numerical values. Especially in the time dimension, we get the error bound, Ohnt−2 for h‐refinement and Oitaliceht/2nt−2nt−2 for nt‐density in the L2 norms. The numerical results obtained show that the proposed numerical algorithm is accurate and computationally efficient for solving time‐fractional telegraph equation. Experiments demonstrate the high convergence rates of the proposed method are consisted with the theoretical values.

Numerical simulation of two‐dimensional and three‐dimensional generalizedKlein–Gordon–Zakharovequations with power law nonlinearity via a meshless collocation method based on barycentric rational interpolation

“…Recently, 2D viscoelastic wave equation and modified Burgers are solved via meshless barycentric Lagrange interpolation method in [55,56]. For more details about barycentric Lagrange interpolation we refer to [2,9,10,12,13,24,30,44,46,74] and references therein.…”

Analysis of the barycentric interpolation collocation scheme for the Burgers equation

“…In this part, we present consistency estimates of the scheme (18) with the collocation method. According to interpolation remainder theorem, we have…”

“…To our knowledge, the works of the error analysis for barycentric interpolation collocation method are relatively sparse. Recently, Yi and Yao [18] put forward a steady barycentric Lagrange interplotaion method and presented error analysis of system for solving the time-fractional telegraph equation. Li [19] provided the error estimate of the barycentric rational interpolation collocation method for the heat conduction equation.…”

A Hybrided Method for Temporal Variable-Order Fractional Partial Differential Equations with Fractional Laplace Operator

“…In addition, finding reliable and powerful numerical and analytical methods for solving FPDEs has been focused on in the last two decades. According to the mathematical literature, fractional partial differential equations have been progressed in various problems in science and engineering such as the Schrödinger, diffusion and telegraph fractional equations [5,[8][9][10][11][12].…”