Simple adaptive grids for 1-D initial value problems (Q1085717)

In solving one-dimensional initial value problems by implicit finite difference methods it is advantageous to use an adaptive grid to provide local regions of high resolution and allow larger time steps to be taken. A simple method of constructing such grids is presented and the benefits are demonstrated by calculations of Sod's shock tube problem [\textit{G. A. Sod}, ibid. 27, 1-31 (1978; Zbl 0387.76063)] and of a supernova explosion.