Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations using Haar wavelet

Abstract

In this paper, we apply Haar wavelet collocation method to solve the linear and nonlinear second-order singularly perturbed differential difference equations and singularly perturbed convection delayed dominated diffusion equations, arising in various modeling of chemical processes. First, we transform delay term by using Taylor expansion and then apply Haar wavelet method. To show the robustness, accuracy and efficiency of the method, three problems of second-order singularly perturbed differential difference equations and three problems of convection delayed dominated diffusion equations have been solved. Also, results are compared with the exact solution of the problems and methods existing in the literature, which confirms the superiority of the Haar wavelet collocation method. We obtained accurate numerical solution of problems by increasing the level of resolutions.

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Correspondence to Akmal Raza.

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Raza, A., Khan, A., Sharma, P. et al. Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations using Haar wavelet. Math Sci (2020). https://doi.org/10.1007/s40096-020-00355-4

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Keywords

  • Haar wavelet
  • Singularly perturbed
  • Convection delayed
  • Differential difference
  • Differential equations
  • Collocation point

Mathematics Subject Classification

  • 65L03
  • 65L10
  • 65L11
  • 65L12
  • 65M70
  • 65N35
  • 42C40
  • 42C42