A study on numerical solution of partial differential equations
Partial differential equations in the physical domain Xn can be solved on a structured numerical grid obtained by mapping a reference grid in the logical region ?n into Xn with a coordinate transformation x(?) : ?n ? Xn. The structured grid concept also gives an alternative way to obtain a numerical solution to a partial differential equation, by solving the transformed equation with respect to the new independent variables ?i on the reference grid in the logical domain ?n. Some notions and relations concerning the coordinate transformations yielding structured grids are discussed in this chapter. These notions and relations are used to represent some conservation-law equations in the new logical coordinates in a convenient form. This article highlights the numerical solution of partial differential equations.