Heat Conduction Equation Amendment To A Class Of Locally Finite Difference Format

The paper have two parts, one is numerical solution of partial di?erential equation,another is submanifold.We discussed the following partial di?erential equation with initial and boundedconditions.. The second derive is replaced of the center di?erence, we attain theequationThe solution of it isThe simple splitting corrected local finite di?erence schemes are gained by splitting of the co-e?cient matrix A. The stability and convergence are discussed about these schemes. A kindof diagonal splitting corrected local finite di?erence schemes is described for the one dimen-sional heat equation. The diagonal splitting corrected implicit scheme and Crank-Nicolsonscheme are unconditionally stable. The stability domain of the diagonal splitting explicitscheme is more larger than the classical explicit method.The theory of minimal surfaces in three-dimensional Riemannian manifold of constantsectional curvature is a classical topic, the research has been developed in large about it.Many geometers are interested in minimal surfaces of three-dimensional manifolds of typeΣ×R, whereΣis a Riamann manifold like the two-sphere S2 or the hyperbolic space H2.When the ambient space is a four-dimensional Riamannian manifold of constant sectionalcurvature, there are many methods to the theory of minimal surfaces. In this case we canstudy the surface according with the K¨ahler structure, there are many examples. For instance,complex surfaces, Lagrange surfaces, totally real surfaces, etc. The associated Jacobianfunction was defined in the paper [CN]. Some properties were given through the associatedJacobian function on the surface S2×S2. This paper also discuss the associated Jacobianfunction, and gain some results.