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Solution of singularly perturbed differential difference equations and convection delayed dominated diffusion equations using Haar wavelet
Mathematical Sciences ( IF 2 ) Pub Date : 2020-10-16 , DOI: 10.1007/s40096-020-00355-4
Akmal Raza , Arshad Khan , Pankaj Sharma , Khalil Ahmad

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.



中文翻译:

利用Haar小波求解奇摄动微分差分方程和对流延迟占优扩散方程。

在本文中,我们采用Haar小波配点法来求解线性和非线性二阶奇摄动对流差分方程和奇摄动对流时滞主导扩散方程,这些方程是在化学过程的各种建模中产生的。首先,我们使用泰勒展开法变换延迟项,然后应用Haar小波方法。为了显示该方法的鲁棒性,准确性和有效性,解决了二阶奇摄动微分差分方程的三个问题和对流延迟支配扩散方程的三个问题。此外,将结果与文献中存在的问题和方法的精确解决方案进行了比较,这证实了Haar小波配置方法的优越性。

更新日期:2020-10-17
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