Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

Herein, we have proposed a scheme for numerically solving hyperbolic partial differential equations (HPDEs) with given initial conditions. The operational matrix of differentiation for exponential Jacobi functions was derived, and then a collocation method was used to transform the given HPDE into a linear system of equations. The preferences of using the exponential Jacobi spectral collocation method over other techniques were discussed. The convergence and error analyses were discussed in detail. The validity and accuracy of the proposed method are investigated and checked through numerical experiments.

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“…Now, using Eqs. 14, (15) and 16, then it is easy to write Now, we tame the collocation procedure for solving Eqs. (17)- (19).…”

Section: Implementation Of the Methodsmentioning

confidence: 99%

“…The HPDEs are used in shaping the vibrational motion of structures (e.g., beams, machines and buildings) and represent basis for fundamental equations of atomic physics [8,9]. Recently, the study of exact and numerical solutions of either hyperbolic or parabolic PDEs has received increasing attention [10][11][12][13][14][15].…”

Section: Introductionmentioning

confidence: 99%

Exponential Jacobi spectral method for hyperbolic partial differential equations

Youssri

Hafez

2019

Math Sci

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“…A spectral collocation scheme based on shifted Jacobi–Gauss collocation approach was proposed by Hafez 12 for 1‐D and 2‐D linear telegraph equation and telegraph equation with nonlinear forcing term. A numerical approach based on the truly meshless methods 13 is proposed to deal with the second‐order 2‐D telegraph equation.…”

Section: Introductionmentioning

confidence: 99%

Linear barycentric rational collocation method for solving telegraph equation

Jin

2021

Math Methods in App Sciences

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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.

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“…where the functions θ 1 (x, t) and Numerical methods such as Jacobi collocation method [12,13], fifth kind Chebyshev method [2], Laguerre spectral method [8], and general orthogonal spectral method [9] are powerful techniques that can be used in applied mathematics and scientific computation to solve different types of differential problems. This work presents an approximation method for a class of Volterra-Fredholm integral equations on the interval [0, L] via the shifted Chebyshev polynomials, and finite difference methods [18][19][20][21][22].…”

Section: Introductionmentioning

confidence: 99%

Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

Youssri

Hafez

2019

Arab. J. Math.

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This work reports a collocation algorithm for the numerical solution of a Volterra-Fredholm integral equation (V-FIE), using shifted Chebyshev collocation (SCC) method. Some properties of the shifted Chebyshev polynomials are presented. These properties together with the shifted Gauss-Chebyshev nodes were then used to reduce the Volterra-Fredholm integral equation to the solution of a matrix equation. Nextly, the error analysis of the proposed method is presented. We compared the results of this algorithm with others and showed the accuracy and potential applicability of the given method.

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Numerical solution of linear and nonlinear hyperbolic telegraph type equations with variable coefficients using shifted Jacobi collocation method

Cited by 18 publications

References 43 publications

Exponential Jacobi spectral method for hyperbolic partial differential equations

Exponential Jacobi spectral method for hyperbolic partial differential equations

Linear barycentric rational collocation method for solving telegraph equation

Chebyshev collocation treatment of Volterra–Fredholm integral equation with error analysis

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