Objective:The study was conducted to (1) find out if visual inspection after acetic acid (VIA)/cervicogram can be used as an alternative to colposcopy and (2) compare the sensitivity and specificity of VIA/cervicogram with conventional Pap smear. Methods: A total of 540 sexually active women aged between 20 and 60 years attending gynecology outpatient (OPD) treatment were included in the study. After the complete evaluation and informed consent, the patients were subjected to the following tests: Pap smear, visual inspection after acetic acid (VIA) application, cervicography, and finally colposcopy. Cervical biopsy was done (a) in women with any of these three tests positive and (b) in patients with unsatisfactory colposcopy. Cervical tissue was obtained with the help of loop electrosurgical excision procedure (LEEP). Biopsies revealing mild dysplasia or worse lesions on histopathology were considered as true positive cases. Biopsies showing chronic cervicitis were considered negative. All results were compiled and subjected to statistical analysis.
Numerical schemes based on off-step discretization are developed to solve two classes of fourth-order time-dependent partial differential equations subjected to appropriate initial and boundary conditions. The difference methods reported here are second-order accurate in time and second-order accurate in space and, for a nonuniform grid, second-order accurate in time and third-order accurate in space. In case of a uniform grid, the second scheme is of order two in time and four in space. The presented methods split the original problem to a coupled system of two second-order equations and involve only three spatial grid points of a compact stencil without discretizing the boundary conditions. The linear stability of the presented methods has been examined, and it is shown that the proposed two-level finite difference method is unconditionally stable for a linear model problem. The new developed methods are directly applicable to fourth-order parabolic partial differential equations with singular coefficients, which is the main highlight of our work. The methods are successfully tested on singular problems. The proposed method is applied to find numerical solutions of the Euler-Bernoulli beam equation and complex fourth-order nonlinear equations like the good Boussinesq equation. Comparison of the obtained results with those for some earlier known methods show the superiority of the present approach.
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