%0 Journal Article
%T A collocation method for the solution of nonlinear one-dimensional parabolic equations
%A J. Rashidinia
%A M. Ghasemi
%A R. Jalilian
%J Mathematical Sciences Quarterly Journal
%D 2010
%I Springer
%X In this paper, we develop a collocation method based on cubic B-spline to the solution of nonlinear parabolic equation $varepsilon u_{xx}=a(x,t)u_{t}+phi(x,t,u,u_{x})$ subject to appropriate initial, and Dirichlet boundary conditions, where $varepsilon >0$ is a small constant. We developed a new two-level three-point scheme of order $O(k^2+h^2)$. The convergence analysis of the method is proved. Numerical results are given to illustrate the efficiency of our method computationally.
%K Cubic B-spline method
%K Nonlinear parabolic equation
%K Singularly perturbed
%K Convection-Diffusion equation
%K Burgers¡¯ equation
%K Convergence analysis.
%U http://mathscience.kiau.ac.ir/Content/Vol4No1/7.pdf