Variable time-step method with coordinate transformation

Numerical stability study and error estimation for two implicit schemes in a moving boundary problem

“…This algorithm calculates the time-step at each time level, iterating until the boundary interface condition is satisfied. In this case, we use the tridiagonal solver instead of the Gaussian elimination, because the first one diminishes the computational effort and is also the most efficient for such matrices [17,18].…”

“…Again the use of Landau's transformation allows us to dissociate the boundary advance from the size of space mesh [17][18][19].…”

The oxygen diffusion problem: Analysis and numerical solution

“…There is, by now, an extensive literature on numerical solutions to the oxygen diffusion problem [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21]. Crank and Gupta [1] considered integral methods, more commonly referred to as heat balance integral methods in relation to heat conduction problems, but these were not valid for small times and also broke down before all the oxygen had been depleted.…”

Comparative study between two numerical methods for oxygen diffusion problem

“…Hansen and Hougaard [6] used an integral equation for the function defining the position of the moving boundary and an integral formula for the concentration distribution. More references to this problem may be found in References [5,[7][8][9][10][11][12].…”