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The purpose of this paper is to design and analyze a robust numerical method for a coupled system of singularly perturbed parabolic delay partial differential equations (PDEs).

Some a priori bounds on the regular and layer parts of the solution and their derivatives are derived. Based on these a priori bounds, appropriate layer adapted meshes of Shishkin and generalized Shishkin types are defined in the spatial direction. After that, the problem is discretized using an implicit Euler scheme on a uniform mesh in the time direction and the central difference scheme on layer adapted meshes of Shishkin and generalized Shishkin types in the spatial direction.

The method is proved to be robust convergent of almost second-order in space and first-order in time. Numerical results are presented to support the theoretical error bounds.

A coupled system of singularly perturbed parabolic delay PDEs is considered and some a priori bounds are derived. A numerical method is developed for the problem, where appropriate layer adapted Shishkin and generalized Shishkin meshes are considered. Error analysis of the method is given for both Shishkin and generalized Shishkin meshes.

India is one of those countries that are severely affected by the COVID-19 pandemic. With the upsurge in the cases, the country recorded high unemployment rates, economic uncertainties and slugging growth rates. This adversely affected the real estate sector in India. As the relation of the housing market with the gross domestic product is quite lasting thus, the decline in housing prices has severely impacted the economic growth of the nation. Hence, the purpose of this paper is to gauge the asymmetric impact of COVID-19 shocks on housing prices in India.

Studies revealed the symmetric impact of macroeconomic variables, and contingencies on housing prices dominate the literature. However, the assumption of linearity fails to apprehend the asymmetric dynamics of the housing sector. Thus, the author uses a nonlinear autoregressive distributed lag model to address this limitation and test the existence of short- and long-run asymmetry.

The findings revealed the long- and short-run asymmetric impact of the COVID-19 outbreak and the peak of the COVID-19 on housing prices. The results indicate that the peak of COVID-19 had a greater impact on housing prices in comparison to the outbreak of COVID-19. This can be explained as prices will revert to normal at a speed of 0.978% with the decline in the number of COVID-19 cases. Whereas the housing prices rise at a rate of 0.714 as a result of government intervention to deal with the ill effects of the COVID-19 outbreak. Moreover, it can be inferred that both the outbreak and peak of COVID-19 will lead to a minimal decline in housing prices, while with the decline in the number of cases and reduction in the impact of the outbreak of COVID, the housing prices will rise at an increasing rate.

To the best of the authors’ knowledge, this is the first study to understand the impact of the outbreak and peak of COVID-19 on the housing prices separately.