Abstract: The generalized wave equation models various
problems in sciences and engineering. In this paper, a new three-time
level implicit approach based on cubic trigonometric B-spline for the
approximate solution of wave equation is developed. The usual finite
difference approach is used to discretize the time derivative while
cubic trigonometric B-spline is applied as an interpolating function in
the space dimension. Von Neumann stability analysis is used to
analyze the proposed method. 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.