Let Ω be a bounded domain in R<sup>2</sup> with smooth boundary and Ω’ be the complementary set of Ω∪ .We consider the Neumann’s problem of parabolic equation as follow;Let τ be time step, t<su...Let Ω be a bounded domain in R<sup>2</sup> with smooth boundary and Ω’ be the complementary set of Ω∪ .We consider the Neumann’s problem of parabolic equation as follow;Let τ be time step, t<sub>k</sub>=k<sub>τ</sub> and u<sup>k</sup>（x）=u（x,t,）. We discrete u/ t of （1） by use of difference and getwhereQ<sup>K</sup>=1/t(u<sup>K</sup>-u<sup>k-1</sup>-t u<sup>k</sup>/ t+f（u<sup>k</sup>）-f(u<sup>k-1</sup>).（2） is a family of Neumann’s boundary value problems of Helmholtz equation. Let E（x,y） be the funda-mental solution to Helmholtz equation, i. e.展开更多
In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equatio...In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.展开更多
文摘Let Ω be a bounded domain in R<sup>2</sup> with smooth boundary and Ω’ be the complementary set of Ω∪ .We consider the Neumann’s problem of parabolic equation as follow;Let τ be time step, t<sub>k</sub>=k<sub>τ</sub> and u<sup>k</sup>（x）=u（x,t,）. We discrete u/ t of （1） by use of difference and getwhereQ<sup>K</sup>=1/t(u<sup>K</sup>-u<sup>k-1</sup>-t u<sup>k</sup>/ t+f（u<sup>k</sup>）-f(u<sup>k-1</sup>).（2） is a family of Neumann’s boundary value problems of Helmholtz equation. Let E（x,y） be the funda-mental solution to Helmholtz equation, i. e.
基金This research was supported by the National Natural Science Foundation of China
文摘In the present paper, a new numerical method for solving initial-boundary value problems of evolutionary equations is proposed and studied, combining difference method with high accuracy with boundary integral equation method. The numerical approximate schemes for both problems on a bounded or unbounded domain in R3 are proposed and their prior error estimates are obtained.
