Abstract
In this paper, weighted finite difference equations for one-dimensional convective diffusion equation are proposed. In these equations, a value of the desired point is represented as the sum of weighted values of the vicinity points. And these weights are obtained from the individual degree polynomial that satisfied the governing equation. This method has the characteristic that we can select at will the vicinity points which have influenced on the desired point according to the state of flow. As the change of value between lattice points is represented by high degree polynomials, this method can obtain higher order accuracy than other finite difference methods and finite element method. By those equations, composed of five vicinity points, it is indicated that the numerical analysis of the governing equation can achieve higher order accuracy than h4, by using non-dimensional lattice spaces Δx=h, Δt=λh2.
