Solving Time Fractional Diffusion-Wave Equation Using Hyperbolic Polynomial B-Splines: A Uniform Grid Approach

Abstract

In this study, we present an efficient numerical scheme based on uniform hyperbolic polynomial B-splines for solving the time-fractional diffusion-wave equation involving the Caputo derivative. This equation models various physical phenomena including anomalous diffusion and complex dynamical behavior. The proposed method ensures a smooth and continuous approximation that effectively captures both local and global features of the solution such as sharp gradients and long-range memory effects. The key advantage of uniform hyperbolic polynomial B-splines lies in their flexibility and high accuracy across the computational domain. Stability and convergence analyses are carried out to confirm the method’s robustness and error control. Finally, numerical results are compared with those reported in existing literature to demonstrate the accuracy and reliability of the scheme as process innovation.