Abstract: The state equations for distributed system are in general partial differential equations(PDEs),which can scarcely be solved analytically because of the increasing demand for more precise simulation of the objects under study and hence much more complexity of the mathematical models.The present paper described the versatility of the numerical method of lines(MOL)Solution of PDEs.In MOL,the author introduced the spline differentiation technique and developed a spectrum of adaptive grid algorithms,that had greatly improved the precision of MOL solutions.The MOL is particularly effective for parabolic PDEs.And the author has proposed a series of algorithms,which enable the MOL to be used in solving certain kinds of PDEs other than parabolic with ease.