科研之友
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摘要
In this paper, we present an hp-version Legendre-Jacobi spectral collocation method for Volterra integro-differential equations with smooth and weakly singular kernels. We establish several new approximation results of the Legendre/Jacobi polynomial interpolations for both smooth and singular functions. As applications of these approximation results, we derive hp-version error bounds of the Legendre-Jacobi collocation method under the H-1-norm for the Volterra integro-differential equations with smooth solutions on arbitrary meshes and singular solutions on quasi-uniform meshes. We also show the exponential rates of convergence for singular solutions by using geometric time partitions and linearly increasing polynomial degrees. Numerical experiments are included to illustrate the theoretical results.
