Inspired by the COVID-19 pandemic, this paper investigates the feasibility of obtaining good convergence results for a nonhomogeneous Volterra-Fredholm integral equation model of the second kind. Volterra-Fredholm integral equations are often used to model infection and recovery of diseases in a population and can be used to model a pandemic or an endemic. This model uses a Volterra-Fredholm integral equation of the second kind to predict the number of individuals recovered from the COVID-19 pandemic in South Africa. The integral model was approximated by using the Gaussian Quadrature Method. The \(\lambda\)ISR model accounts for many variables of the pandemic including the number of initially infected individuals I0, susceptible individuals S0, and removed individuals R0. It also accounts for the initial recovery rate \(\gamma\), the infectivity of the virus \(\beta\) , removal rate \(\mu\) , and the total population of South Africa N. In addition to these, we also considered blood type S (x), and the rh factor \(\lambda\)(x) . The model was constructed in “person-days,” which is the combined variable of time (t, days) and the number of individuals (x). Specific blood types and presence of the rh factor have been shown to have varying susceptibility to infection and severity of infection (requiring intubation), therefore this was an important parameter for this model [1,2].

The two major parties in Sri Lanka are putting forward an increased number of minority candidates in order to prevent the minorities from voting for ethnically-/religiously-based minority parties. The proportional representative (PR) system that was introduced in 1989 was initially considered as a disadvantage to the minorities. However, the PR system has benefited the minorities and has not brought any expected benefits to the major parties. More minority candidates are getting elected, but the votes of the minorities are getting split, and therefore there is no net gain to the two major parties. In fact, there is evidence to say that parties that are taking a more nationalistic approach are doing better than the parties that are projecting a more inclusive image. Appealing to the minorities has alienated the majority, Sinhalese, so the major parties are moving towards more radical extremist nationalistic platforms. Wilcoxon Rank Sum test was used for this analysis, the samples that were taken were independent and no assumptions were made on the probability distributions other than the fact that they are continuous.

The objective of this work was to find the numerical solution of the Dirichlet problem for the Helmholtz equation for a smooth superellipsoid. The superellipsoid is a shape that is controlled by two parameters. There are some numerical issues in this type of an analysis; any integration method is affected by the wave number k, because of the oscillatory behavior of the fundamental solution. In this case we could only obtain good numerical results for super ellipsoids that were more shaped like super cones, which is a narrow range of super ellipsoids. The formula for these shapes was:where n varied from 0.5 to 4. The Helmholtz equation, which is the modified wave equation, is used in many scattering problems. This project was funded by NASA RI Space Grant for testing of the Dirichlet boundary condition for the shape of the superellipsoid. One practical value of all these computations can be getting a shape for the engine nacelles in a ray tracing the space shuttle. We are researching the feasibility of obtaining good convergence results for the superellipsoid surface. It was our view that smaller and lighter wave numbers would reduce computational costs associated with obtaining Galerkin coefficients. In addition, we hoped to significantly reduce the number of terms in the infinite series needed to modify the original integral equation, all of which were achieved in the analysis of the superellipsoid in a finite range. We used the Green's theorem to solve the integral equation for the boundary of the surface. Previously, multiple surfaces were used to test this method, such as the sphere, ellipsoid, and perturbation of the sphere, pseudosphere and the oval of Cassini Lin and Warnapala [9], Warnapala and Morgan [10].

In this paper, the Galerkin method is used to numerically solve the exterior boundary value problem for the Radiosity equation for a spherical shape, specifically the Spherical Rhombus. The Radiosity equation is a mathematical model for the brightness of a collection of one or more surfaces when their reflectivity and emissivity are given. On planet Mars the surface emissivity is closely related to its surface temperature. The Radiosity of a surface is the rate at which the energy leaves that surface; it includes the energy emitted by a surface as well as the energy reflected from other surfaces.

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