Cui, Xia An alternating-direction implicit Galerkin method and the analysis for 3-dimensional nonlinear integro-differential equation for hyperbolic type. (Chinese. English summary) Zbl 0969.65125 J. Shandong Univ., Nat. Sci. Ed. 35, No. 2, 135-143 (2000). Summary: The alternating direction implicit (ADI) Galerkin scheme for 3-dimensional nonlinear hyperbolic integro-differential equation is studied. By using summing by part and other priori estimate techniques such as inductive hypothesis reasoning, the stability and convergence properties for both Galerkin and ADI Galerkin schemes are demonstrated; the optimal \(H^1\)-norm and \(L^2\)-norm estimates are obtained. MSC: 65R20 Numerical methods for integral equations 45K05 Integro-partial differential equations 45G10 Other nonlinear integral equations Keywords:finite element method; error bound; alternating direction implicit Galerkin scheme; nonlinear hyperbolic integro-differential equation; stability; convergence PDFBibTeX XMLCite \textit{X. Cui}, J. Shandong Univ., Nat. Sci. Ed. 35, No. 2, 135--143 (2000; Zbl 0969.65125)