三维双曲方程非齐次边值问题的推广型LOD有限差分格式

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L^2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△t^4，从而使△t的取法有更大的灵活性．

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

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 be 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 de-compose and the intermediate boundary condition is difficult to determine. The convergence order of the LOD scheme is sec-ond order accuracy in discrete Lz norm. Compared with parabolic differential equations the order of disturbed term of the scheme is O(△t4), and At can be selected freely.