中文摘要：

介绍了偏微分方程求解过程中级数方法的使用,比如在波动方程、热传导方程和Laplace方程的求解上,特别讨论了使用级数方法所得的解的表达式与其他方法所得到的解是一致的。另外,对于实际问题中出现的一些非线性方程或离散形式的方程,这里也尝试去求解。

英文摘要：

This paper uses the series method to investigate the solutions of PDE,such as wave equations,heat equations and Laplace equations.The consistency of solutions for these equations is studied particularly.Besides,the series solutions of the Cauchy problems for some nonlinear equations with physical background are also discussed.