Showing papers on "Meshfree methods published in 1975"
22 citations
01 Jan 1975
TL;DR: In this article, the connection between the finite difference like methods and the methods based on initial value problems for ODEs is highlighted, and the use of deferred corrections leads to the solution of the same equations using an extrapolation procedure based on second order schemes.
Abstract: Publisher Summary This chapter highlights the connection between the finite difference like methods and the methods based on initial value problems forordinary differential equations (ODE). The formulation of the systems of equations stemming from different versions of finite difference methods or finite element methods, as presented in the theory, is not the entire story of the numerical solution of boundary value problems for ODE. An essential part of the process is the solution of the derived systems of equations. There are many ways to solve these systems, a variety of direct and iterative methods. Using the finite difference method, the initial value problem for equations can be solved by a second order method without automatic step selection. The use of the deferred corrections leads to the solution of the same equations using an extrapolation procedure based on second order schemes. Another point is that the second order method stemming from the elimination method needs a relatively very small number of operations. Iterative procedures are not used when solving boundary value problems for ODEs.
7 citations
TL;DR: In this article, the possibility of studying the gravity field outside local disturbing masses by applying the methods of numerical analysis, in particular the finite difference method, was shown, and the possibility was shown of studying gravity field inside local disturbing mass.
Abstract: The possibility is shown of studying the gravity field outside local disturbing masses by applying the methods of numerical analysis, in particular the finite difference method.
3 citations
01 Apr 1975
TL;DR: In this paper, the numerical properties of a selected number of finite element and finite difference methods for geotechnical engineering problems were examined, and the numerical and physical properties of these schemes were examined.
Abstract: : A large number of schemes using the finite element (FE) and finite difference (FD) methods have been proposed. Numerical and physical properties of these schemes, vital for their use as general procedures and significant from the viewpoint of the user, are often not examined adequately. One of the aims of this study was to examine numerical properties of a selected number of schemes for problems relevant to geotechnical engineering.
2 citations