The splitting extrapolation is an important technique for solving multidimensionalproblems.In the case that error u<sup>h</sup>-u has an asymptotic expansion of form Σc<sub>α</sub>h<sup&g...The splitting extrapolation is an important technique for solving multidimensionalproblems.In the case that error u<sup>h</sup>-u has an asymptotic expansion of form Σc<sub>α</sub>h<sup>2α</sup>,whereα=（α<sub>1</sub>,…,α<sub>s</sub>） and h<sup>α</sup>=h<sub>1</sub><sup>α<sub>1</sub></sup>,…h<sub>s</sub><sup>α<sub>s</sub></sup>,the method gives an approximation involving less computerstorage and less computational work in comparison with the classical Richardson extrapolation.In this paper we present a recurrence rule of the splitting extrapolation and discuss itsapplications in the fields of multiple integrals,multidimensional integral equations,partialdifferential equations and singular perturbation problems.展开更多
文摘The splitting extrapolation is an important technique for solving multidimensionalproblems.In the case that error u<sup>h</sup>-u has an asymptotic expansion of form Σc<sub>α</sub>h<sup>2α</sup>,whereα=（α<sub>1</sub>,…,α<sub>s</sub>） and h<sup>α</sup>=h<sub>1</sub><sup>α<sub>1</sub></sup>,…h<sub>s</sub><sup>α<sub>s</sub></sup>,the method gives an approximation involving less computerstorage and less computational work in comparison with the classical Richardson extrapolation.In this paper we present a recurrence rule of the splitting extrapolation and discuss itsapplications in the fields of multiple integrals,multidimensional integral equations,partialdifferential equations and singular perturbation problems.
