Two Types Of Numerical Solution Of Partial Differential Equations

This paper mainly includes two parts.The first part includes the introduction of the basic properties of the KdV Equation and several simulation methods which are usually used for calculating the KdV Equation, and the Spectral Method which is used in this paper is also introduced. According to the discrete Fourier transform, a refined theory of Spectral Method is presented under the special boundary conditions and the numerical computation obtains a good approximation effect. The second part includes the discussion of The Finite Element Numerical Method for Poisson Equation in sector area. As the effort of partition a sector area is not perfect by using the triangular and quadrilateral partition, polar transformation is used to transfer the sector area to the rectangular area. Under the definite condition for the angle of the sector area, we can prove the existence and uniqueness of the solution. Then we use Bilinear Finite Element to derive numerical calculation and analysis the error estimation.