Redefined cubic B-splines collocation method for solving convection–diffusion equations

In this work, we discuss collocation method based on redefined cubic B-splines basis functions for solving convection–diffusion equation with Dirichlet’s type boundary conditions. Stability of this method has been discussed and shown that it is unconditionally stable. The developed method is tested on various problems and the numerical results are reported in tabular form. The computed results are compared wherever possible with those already available in literature. The method is shown to work for Péclet number ⩽ 10. Easy and economical implementation process is the strength of it. This method can be easily extended to handle non-linear convection–diffusion partial differential equations.