Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider the numerical solution of the time-fractional diffusion-wave equation. Essentially, the time fractional diffusion-wave equation differs from the standard diffusion-wave equation in the time derivative term.  propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. The convergence of the method is rigorously established. Numerical tests are carried out to confirm the theoretical results.
['Yin Yang', 'Yanping Chen', 'Yunqing Huang', 'Huayi Wei']
I am writing a research paper on a idea Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis
[{"from": "human", "value": "I am writing a research paper on a idea Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: ,  consider the numerical solution of the time-fractional diffusion-wave equation. Essentially, the time fractional diffusion-wave equation differs from the standard diffusion-wave equation in the time derivative term.  propose a spectral collocation method in both temporal and spatial discretizations with a spectral expansion of Jacobi interpolation polynomial for this equation. The convergence of the method is rigorously established. Numerical tests are carried out to confirm the theoretical results."}]