The application of cubic trigonometric B-spline to the numerical solution of the hyperbolic problems

In this paper, a collocation finite difference scheme based on new cubic trigonometric B-spline is developed and analyzed for the numerical solution of a one-dimensional hyperbolic equation (wave equation) with non-local conservation condition. The usual finite difference scheme is used to discretize the time derivative while a cubic trigonometric B-spline is utilized as an interpolation function in the space dimension. The scheme is shown to be unconditionally stable using the von Neumann (Fourier) method. The accuracy of the proposed scheme is tested by using it for several test problems. The numerical results are found to be in good agreement with known exact solutions and with existing schemes in literature.