Variable time-step method with coordinate transformation

The variable time-step methods for solving moving boundary problems are presented by transforming the variable space domain. This results in dissociating the mode of advancement of the boundary from the size of the space mesh. That is, a small movement of the moving boundary may be chosen for computing the time interval while the space domain is subdivided into larger space meshes. As a consequence, an enormous amount of saving in computer time may be achieved by using the proposed method. Two sample problems are selected for the illustration of the method.