in this paper , the quintic b-spline collocation scheme is employed to approximate numerical solution of the kdv-like rosenau equation . this scheme is based on the crank-nicolson formulation for time integration and quintic b-spline functions for space integration . the unconditional stability of the present method is proved using von- neumann approach . since we do not know the exact solution...

[1] We present exact analytical solutions for a one-dimensional diffusion problem coupled with the precipitation-dissolution reaction AðaqÞ þ BðaqÞ Ð MðsÞ and feedback of porosity change. The solutions are obtained in the form of traveling waves and describe spatial and temporal evolutions of solute concentration, porosity, and mineral distribution for a set of initial and boundary conditions. ...