# Approximation of a timewise dependent function in the inverse one-dimensional telegraph equation

Document Type : Original Paper

Authors

Department of Mathematics, University of Science and Technology of Mazandaran, Behshahr, Iran

Abstract

In this article, we study the linear inverse problem for approximating a timewise-dependent

function in the second-order hyperbolic equation. To solve the problem, information such as Neumann

boundary conditions along with an integral condition and initial conditions at the initial moment and the

final instant have been provided. In the first step, we show that this problem has a unique solution. Then,

we change the main problem into a new one and then we present the spectral approximation based on

the Ritz-collocation method to recover the unknown functions. Discretization of the problem by using

the presented technique leads to a linear system of algebraic equations, which Tikhonov’s regularization

method is used to obtain stable solutions. The results of the numerical simulation confirm the high accuracy

and stability of the approximate solution.

Keywords

Main Subjects

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### History

• Receive Date: 12 March 2023
• Revise Date: 07 June 2023
• Accept Date: 19 June 2023