Numerical solution of second order one dimensional hyperbolic equation by exponential B-spline collocation method

In this paper, we propose a method based on collocation of exponential B-splines to obtain numerical solution of nonlinear second order one dimensional hyperbolic equation subject to appropriate initial and Dirichlet boundary conditions. The method is a combination of B-spline collocation method in space and two stage, second order strong-stability-preserving Runge–Kutta method in time. The proposed method is shown to be unconditionally stable. The efficiency and accuracy of the method are successfully described by applying the method to a few test problems.