An Efficient Algorithm Based on Extrapolation for the Solution of Nonlinear Parabolic Equations

摘要

Two numerical procedures are developed to approximate the solution of one-dimensional parabolic equations using extrapolated collocation method. By defining two different end conditions and forcing cubic spline to satisfy the interpolation conditions along with one of the end conditions, we obtain fourth- (CBS4) and sixth-order (CBS6) approximations to the solution in spatial direction. Also in time direction, a weighted finite-difference discretization is used to approximate the solution at each time level. The convergence analysis of the methods is discussed in detail and some error bounds are obtained theoretically. Finally, some different examples of Burgers’ equations with applications in fluid mechanics as well as convection–diffusion problems with applications in transport problems are solved to show the applicability and good performance of the procedures.