A numerical technique for solving singularly perturbed differential-difference equations and singularly perturbed convection delayed dominated diffusion equations using Jacobi wavelet

Abstract

This paper is concerned with the numerical solution of singularly perturbed differential-difference equations (SPDDE) and singularly perturbed convection delayed dominated diffusion equations (SPCDDDE) arising in the modelling of various chemical phenomena. We have approximated the delayed term by Taylor series expansion and then employed the Jacobi wavelet method. We have solved two examples of each SPDDE and SPCDDDE and compared our results with the results of existing methods and found that our method gives better accuracy. The numerical outcomes show that as we increase the values of convergence parameters i.e., degree of Jacobi polynomial ($M$) or resolution level ($k$) or both, the approximate solution converges to the exact solution. To the best of our knowledge, the present method is one of the first in literature that makes use of polynomial based wavelet to find the approximate solution of SPDDE and SPCDDDE.