Higher-order tension spline-based numerical technique for time fractional reaction-diffusion wave equation with damping

This article presents an efficient numerical technique based on tension spline for the time fractional reaction-diffusion wave equation with damping. The proposed method involves the tension factor associated with the splines. Moreover, the order of accuracy relies on the suitable choice of two parameters that increment it from two to four, which is explained conceptually and numerically. The time-fractional derivative is considered as Caputo derivative. We have shown that our technique is unconditionally stable and convergent through rigorous analysis. Two test examples show the numerical scheme's effectiveness and verify theoretical results.