In this paper, we propose a new three-level implicit nine point compact finite difference formulation of O(k2 + h4) based on non-polynomial tension spline approximation in r-direction and finite difference approximation in t-direction for the numerical solution of one dimensional wave equation in polar co-ordinates. We describe the mathematical formulation procedure in details and also discuss the stability of the method. Numerical results are provided to justify the usefulness of the proposed method.
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Gopal et al. (2013) studied this question.