Exponentially Fitted Tension Spline Method For Singularly Perturbed Time Delay Reaction Diffusion Problems

Abstract

In this study, exponentially fitted tension spline method is presented for solving singularly perturbed time delay reaction-diffusion problems. Crank-Nicolson method is used for time discretization and exponentially fitted tension spline method is applied for spatial discretiza tion. Using the comparison principle and solution bound, the scheme’s stability is analyzed. The scheme’s uniform convergence is proved. The suggested approach is proven to be uni formly convergent in space and time, with virtually second order in both direction. The scheme’s theoretical analysis is supported by numerical test examples for various values of ε and mesh size.