Integrals and series of special functions
Integrals and series of special functions
Analysis for one-dimensional time-fractional Tricomi-type equations by LDG methods
Numerical Algorithms
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The boundary element spline collocation method is studied for the time-fractional diffusion equation in a bounded two-dimensional domain. We represent the solution as the single layer potential which leads to a Volterra integral equation of the first kind. We discretize the boundary integral equation with the spline collocation method on uniform meshes both in spatial and time variables. In the stability analysis we utilize the Fourier analysis technique developed for anisotropic pseudodifferential equations. We prove that the collocation solution is quasi-optimal under some stability condition for the mesh parameters. We have to assume that the mesh parameter in time satisfies $(h_t=c h^{\frac{2}{\alpha}})$ , where (h) is the spatial mesh parameter.