A SUPERCONVERGENT DISCONTINUOUS GALERKIN METHOD FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS, SMOOTH AND NON-SMOOTH KERNELS

作者：Mustapha Kassem^*

来源：Mathematics of Computation, 2013, 82(284): 1987-2005.

DOI：10.1090/s0025-5718-2013-02689-0

• Integro-differential equation
• weakly singular kernel
• smooth kernel
• DG time-stepping
• error analysis
• variable time steps

We study the numerical solution for Volerra integro-differential equations with smooth and non-smooth kernels. We use an h-version discontinuous Galerkin (DG) method and derive nodal error bounds that are explicit in the parameters of interest. In the case of non-smooth kernel, it is justified that the start-up singularities can be resolved at superconvergence rates by using non-uniformly graded meshes. Our theoretical results are numerically validated in a sample of test problems.

• 出版日期2013-10
• 单位中国石油大学（北京）