Two finite difference schemes for time fractional diffusion‐wave equation

Time fractional diffusion‐wave equations are generalizations of classical diffusion and wave equations which are used in modeling practical phenomena of diffusion and wave in fluid flow, oil strata and others. In this paper we construct two finite difference schemes to solve a class of initial‐boundary value time fractional diffusion‐wave equations based on its equivalent partial integro‐differential equations. Under the weak smoothness conditions, we prove that our two schemes are convergent with first‐order accuracy in temporal direction and second‐order accuracy in spatial direction. Numerical experiments are carried out to demonstrate the theoretical analysis.