Numerical solutions of one-dimensional non-linear parabolic equations using Sinc collocation method

Nonlinear parabolic equations; Singularly perturbed equations; Sinc collocation method; Convergence analysis Abstract We propose a numerical method for solving singularly perturbed one-dimensional nonlinear parabolic problems. The equation converted to the nonlinear ordinary differential equation by discretization first in time then subsequently in each time level we use the Sinc collocation method on the ordinary differential equation. The convergence analysis of proposed technique is discussed, and it is shown that the approximate solution converges to the exact solution at an exponential rate as well. We know that the conventional methods for these types of problems suffer due to decreasing of perturbation parameter, but the Sinc method handles such difficulty. For efficiency and accuracy of the method, we validate the proposed method by several examples. The numerical results confirm the theoretical behavior of the rates of convergence. 2014 Production and hosting by Elsevier B.V. on behalf of Ain Shams University. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).