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中文摘要：
针对二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．证明了此种LOD有限差分格式按照离散L^2模具有二阶收敛精度．数值算例表明计算效果良好．
英文摘要：
An improved locally one-dimensional finite difference scheme is presented for two dimensional nonhomogenerous hyperbolic equations with 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 decompose and the intermediate boundary condition is difficult to determine. The convergence order of the LOD scheme is O（τ^2 ＋h^2） in discrete L2 norm. Numerical example indicates the results is very satisfactory.
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