The Immersed Boundary (IB) Methods have been proven to besuitable to handle complex geometrical boundaries, moving boundaries andfluid-structure interactions, etc, since only the fixed Cartesian grids arerequired. C. S. Peskin first introduced this method in the 1970s with a flatdevelopment period. In resent years, numerous modifications and refinementshave been proposed and variants of this approach now exist. In this study,two different types of IB methods are introduced, the Continuous ExplicitForcing Method (CEFM) and the Discrete Implicit Forcing Method (DIFM). InCEFM, the forcing terms are introduced into the controlling equations toreplace the boundary conditions on the surfaces and the controllingequations can be explicitly solved. In DIFM, the forcing effect isconsidered in the boundary conditions on the so-called ghost cells insidethe surfaces directly. To promote the computational accuracy near the solidsurface, this study firstly modifies the CEFM and then proposes a newtreatment called a predicted DIFM. They have been validated by numericalsimulations of the uniform incompressible flow past a cylinder. The resultssuggest that the present modification for CEFM leads to a higher accuracynear solid surfaces than the original one, which uses forcing terms in astaggered time-level comparing the time-level of velocities. Moreover, only1-order or even less of accuracy near surfaces can be obtained since thecontrolling equations are discretized by a 2-order scheme. Therefore, it maybe not useful for this type of methods to refine the meshes near thesurfaces to obtain a higher accuracy. Meanwhile, the DIFM can obtain muchmore accurate results especially and the assumption of pseudo-coincidentpoints is proven to be effective to promote the accuracy from 1-order to2-order with fine grids, even if the linear assumption of velocitydistribution near solid surfaces remains. Hence, the predicted DIFM isproven to lead less numerical errors and a faster convergence, even thoughit can't promote a higher order of accuracy. Moreover, the overallaccuracies are not affected obviously by the different methods and goodresults are obtained in simulations of the cylinder case. Further researchesare performed in the cases with moving boundaries, more complex geometricalboundaries and fluid-structure interactions.