This note is concerned with the problem of determining approximate solutions of Fredholm integral equations of the second kind. Approximating the solution of a given integral equation by means of a polynomial, an over-determined system of linear algebraic equations is obtained involving the unknown coefficients, which is finally solved by using the least-squares method. Several examples are examined in detail.
In this work, we present and discuss the approaches, that are used for modeling and surveillance of dynamics of infectious diseases by considering the early stage asymptomatic and later stage symptomatic infections. We highlight the conceptual ideas and mathematical tools needed for such infectious disease modeling. We compute the basic reproduction number of the proposed model and investigate the qualitative behaviours of the infectious disease model such as, local and global stability of equilibria for the non-delayed as well as delayed system. At the end, we perform numerical simulations to validate the effectiveness of the derived results.
The problem of scattering of obliquely incident surface water waves by small undulation on a sea-bed is considered for solution by assuming that the bed is composed of porous material of a specific type. The reflection and transmission coefficients are determined approximately after assuming a perturbation analysis in conjunction with the Fourier transform technique, in terms of the first order of smallness of an undulation parameter ε, introduced in the description of the sea-bed. The special case of a patch of sinusoidal ripples on the bed is handled in detail and numerical results are presented graphically.
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