Showing papers on "Meshfree methods published in 1965"

Steady heat flow ii: numerical methods

Abstract: This chapter discusses the various numerical methods for determining steady heat flow. It also discusses the numerical methods based on a finite difference form of the equation of heat conduction. This also affords a convenient opportunity for a general introduction to finite difference methods that are particularly important for transient heat flow. The finite difference method is first explained in some detail for the case of one-dimensional heat flow and then extended to the two-dimensional case in which not many new points arise. First, a method is presented for explicitly solving systems of finite difference equations provided that these are linear in the temperatures. These restrictions can be dropped in the other two methods treated: the methods of successive approximations and of relaxation. In particular, the section on truncation errors is relevant to all the finite difference methods. For the sake of convenience, these methods are explained mainly for equations that are linear in the temperatures but extensions to nonlinear cases can easily be made.