Abstract:
In this paper, the sixth-order compact finite difference method is presented for solving singularly perturbed 1D reaction–diffusion
problems. The derivative of the given differential equation is replaced by finite difference approximations. Then, the given difference
equation is transformed to linear systems of algebraic equations in the form of a three-term recurrence relation, which can easily be
solved using a discrete invariant imbedding algorithm. To validate the applicability of the proposed method, some model examples
have been solved for different values of the perturbation parameter and mesh size. Both the theoretical error bounds and the numerical
rate of convergence have been established for the method. The numerical results presented in the tables and graphs show that the
present method approximates the exact solution very well.
