Abstract
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations. The advantages of this technique are that not only is the convergence rate of Sinc approximation exponential but the computational speed also is high due to the use of the Haar operational matrices. This technique is used to convert the problem to the solution of linear algebraic equations via expanding the required approximation based on the elements of Sinc functions in space and Haar functions in time with unknown coefficients. To analyze the efficiency, precision, and performance of the proposed method, we presented four examples through which our claim was confirmed.
Highlights
In recent years, the field of hyperbolic partial differential equations has attracted the attention of scientists in several areas and has been used to solve many actual problems modeled in mathematical physics, such as the vibrations of structures, fluid mechanics, and atomic physics [1].The telegraph equation has typically been used for transmission and propagation of electrical signals [2], wave propagation model [3], random walk theory [4], and so forth
The present study investigates the Haar-Sinc collocation method for the solution of the hyperbolic partial telegraph equations
The field of hyperbolic partial differential equations has attracted the attention of scientists in several areas and has been used to solve many actual problems modeled in mathematical physics, such as the vibrations of structures, fluid mechanics, and atomic physics [1]
Summary
The field of hyperbolic partial differential equations has attracted the attention of scientists in several areas and has been used to solve many actual problems modeled in mathematical physics, such as the vibrations of structures (e.g., buildings, beams, and machines), fluid mechanics, and atomic physics [1]. The numerical approximation based on differential transform method (DTM) was considered to solve telegraph equation [5]. It is essential to be said that [17,18,19,20,21,22,23,24] have previously used the Haar and Sinc functions separately for solving optimal control problems and some nonlinear ordinary differential equations. Based on the properties of orthogonal Sinc functions, it is apparent that the convergence rate of approximation is exponential [21] By using this property, the authors of [22,23,24] studied the Sinc collocation method for solving nonlinear singular equations like Thomas-Fermi, Lane-Emden, and Blasius equations.
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