三维双曲方程非齐次边值问题的推广型LOD有限差分格式

Improved locally one-dimensional finite difference scheme for three dimensional hyperbolic equations with nonhomogenerous boundary condition

针对三维非齐次双曲方程第一边值问题提出了一种新型的LOD有限差分格式,此格式能够将高维问题完全分解为一系列一维问题进行求解,克服了LOD格式源项难以分解、过渡层条件不易确定的缺陷.证明了该LOD有限差分格式按照离散L2模具有二阶收敛精度,与抛物型方程相比,源项的扰动达到了Δt4,从而使Δt的取法有更大的灵活性.

An improved locally one-dimensional finite difference scheme is presented for three dimensional nonhomogenerous hyperbolic equations with the first boundary value condition. High dimensional equation can he solved by decomposing to a series of one dimensional equations with this scheme. The scheme overcomes the defects that the source term is hard to decompose and the intermediate boundary condition is difficult to determine. The convergence order of the LOD scheme is second order accuracy in discrete L^2 norm. Compared with parabolic differential equations the order of disturbed term of the scheme is O（Δt4 ）, and Δt can be selected freely.