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Numerical solution of second-order hyperbolic telegraph equation via new cubic trigonometric B-splines approach. (English) Zbl 1427.65295

Summary: This paper presents a new approach and methodology to solve the second-order one-dimensional hyperbolic telegraph equation with Dirichlet and Neumann boundary conditions using the cubic trigonometric B-spline collocation method. The usual finite difference scheme is used to discretize the time derivative. The cubic trigonometric B-spline basis functions are utilized as an interpolating function in the space dimension, with a \(\theta\) weighted scheme. The scheme is shown to be unconditionally stable for a range of \(\theta\) values using the von Neumann (Fourier) method. Several test problems are presented to confirm the accuracy of the new scheme and to show the performance of trigonometric basis functions. The proposed scheme is also computationally economical and can be used to solve complex problems. The numerical results are found to be in good agreement with known exact solutions and also with earlier studies.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
65D07 Numerical computation using splines
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
74S20 Finite difference methods applied to problems in solid mechanics
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References:

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