In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local trunc...In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.展开更多
In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular ...In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).展开更多
本文给出了一个解 m 维抛物型偏微分方程的差分格式,它含有两个参数α,β,当α≥1/2,β≥m 时,它是三层显格式,绝对稳定。它的截断误差为 o(τ+h^2),τ=△t,h=△x.本文可看成是[1]的格式的推广。对于二维情形,本文用数值例子验算了格式...本文给出了一个解 m 维抛物型偏微分方程的差分格式,它含有两个参数α,β,当α≥1/2,β≥m 时,它是三层显格式,绝对稳定。它的截断误差为 o(τ+h^2),τ=△t,h=△x.本文可看成是[1]的格式的推广。对于二维情形,本文用数值例子验算了格式的稳定性与精确度。展开更多
文摘In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.
基金This work is supported by the National Fujian Province Nature Science Research Funds
文摘In this paper, we consider a singular perturbation elliptic-parabolic partial differential equation for periodic boundary value problem, and construct a difference scheme. Using the method of decomposing the singular term from its solution and combining an asymptotic expansion of the equation, we prove that the scheme constructed by this paper converges uniformly to the solution of its original problem with O(r+h2).
