Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations
- PDF / 1,824,895 Bytes
- 14 Pages / 595.276 x 790.866 pts Page_size
- 11 Downloads / 188 Views
ORIGINAL RESEATCH
Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations using Haar wavelet Akmal Raza1 · Arshad Khan1 · Pankaj Sharma2 · Khalil Ahmad3 Received: 22 December 2018 / Accepted: 25 September 2020 © Islamic Azad University 2020
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. Keywords Haar wavelet · Singularly perturbed · Convection delayed · Differential difference · Differential equations · Collocation point Mathematics Subject Classification 65L03 · 65L10 · 65L11 · 65L12 · 65M70 · 65N35 · 42C40 · 42C42
Introduction It appears from literature that using certain cautions, simple delayed mass-action systems can be used in chemical miniature. The Brown and DO miniature are indications in this direction [7]. The greatest serious magnificent problem is * Akmal Raza [email protected] Arshad Khan [email protected] Pankaj Sharma [email protected] Khalil Ahmad [email protected] 1
Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India
2
Department of Mathematics, Zakir Husain Delhi College, University of Delhi, New Delhi, Delhi 110002, India
3
Department of Mathematics, Al-Falah University, Faridabad 121004, India
the treatment of fully unpredictable mechanisms operating near equilibrium in which systems require properly distributed delays. In a similar way, hypoglycemia remains a big barrier to the intensification of insulin therapy of a diabetic patient. Continuous glucose-monitoring devices measuring interstitial fluid glucose exhibit time delays when compared to capillary blood glucose. Short delays exist due to diffusion through glucose membrane, as the process of diffusion often depends upon membrane thickness [28]. Lower levels of glycated hemoglobin are unfortunately associated with an increased risk of hypoglycemia [18]. There are many reasons why we might wish to develop the class of miniature available among scholars to include delayed variable formulations. In several recent chemical miniature theories, delay differential equations (DDEs) are being used in place of the usual mass action ordinary differential equations (ODE) [44]. DDEs present important opportuni
Data Loading...
