Numerical Solution of second order hyperbolic telegraph equation via new\n Cubic Trigonometric B-Splines Approach

2015/10/30 by Tahir Nazir, Nazir, Tahir, Muhammad Abbas +5
Mathematics · #Differential Equations and Numerical Methods #FOS: Mathematics #Fractional Differential Equations Solutions #Numerical Analysis (math.NA) #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.1510.09051

openalex publication_date 2015/10/30 · openalex created_date 2022/10/05 · openalex updated_date 2026/07/28

Abstract

This paper presents a new approach and methodology to solve the second order\none dimensional hyperbolic telegraph equation with Dirichlet and Neumann\nboundary conditions using the cubic trigonometric B-spline collocation method.\nThe usual finite difference scheme is used to discretize the time derivative.\nThe cubic trigonometric B-spline basis functions are utilized as an\ninterpolating function in the space dimension, with a weighted scheme. The\nscheme is shown to be unconditionally stable for a range of values using the\nvon Neumann (Fourier) method. Several test problems are presented to confirm\nthe accuracy of the new scheme and to show the performance of trigonometric\nbasis functions. The proposed scheme is also computationally economical and can\nbe used to solve complex problems. The numerical results are found to be in\ngood agreement with known exact solutions and also with earlier studies.\n

Related

• A collocation method for numerical solution of Telegraph equation
• A new numerical algorithm for the solutions of hyperbolic partial differential equations in (2+1)-dimensional space
• An algorithm based on a new DQM with modified exponential cubic B-splines for solving hyperbolic telegraph equation in (2+1) dimension
• Numerical and approximate solutions for two-dimensional hyperbolic telegraph equation via wavelet matrices
• The application of cubic trigonometric B-spline to the numerical\n solution of time-fractional telegraph equation