Hybrid cubic B-spline collocation method for solving one-dimensional wave equation

The one-dimensional wave equation models various problems in sciences and engineering. In this work, a new three-time level implicit approach based on hybrid cubic B-spline is developed to approximate the solution of wave equation. The central finite difference approximation is used to discretize the time derivative while hybrid cubic B-spline is applied as an interpolating function in the space dimension. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.