ABSTRACT
This chapter shows the use of finite differences for solving differential equations relating the transverse load to the deflection in beams and slabs results in a system of simultaneous linear equations. The method of finite differences can be used in the analysis of thin plates. Two different problems arise depending on the type of loading. The numerical solution by finite differences generally requires replacing the derivatives of a function by difference expressions of the function at the nodes. The differential equation governing the displacement or stress is applied in a difference form at each node, relating the displacement at the given node and at nodes in its vicinity to the external applied load. This usually provides a sufficient number of simultaneous equations for the displacements or stresses to be determined. The finite-difference coefficients of the equations applied at nodes on, or close to, the boundary have to be modified, compared with the coefficients used at interior points.
