Multiple perturbed collocation tau method for solving nonlinear integro-differential equations

ABSTRACT: The purpose of the study was to investigate the numerical solution of non-linear Fredholm and Volterra integro-differential equations by the proposed method called Multiple Perturbed Collocation Tau Method (MPCTM). We assumed a perturbed approximate solution in terms of Chebyshev polynomial basis function and then determined the derivatives of the perturbed approximate solution which are then substituted into the special classes of the problems considered. Thus, resulting into n-folds integration, the resulting equation is then collocated at equally spaced interior points and the unknown constants in the approximate solution are then obtained by Newton's method which are then substituted back into the approximate solution.Illustrative examples are given to demonstrate the efficiency, computational cost and accuracy of the method. The results obtained with some numerical examples are compared favorable with some existing numerical methods in literature and with the exact solutions where they are known in closed form

A survey of facial nerve dessection techniques in benign parotid surgery among maxillofacial and ear, nose, and throat surgeons in Nigeria

Objective: The aim of the present study is to identify the facial nerve dissection technique routinely used during parotidectomy for benign parotid tumors by Nigerian Oral and Maxillofacial (OMF) and Ear; Nose; and Throat (ENT) Surgeons. Materials and Methods: A questionnaire-based study was conducted among Oral and Maxillofacial and Ear; Nose; and Throat Surgeons in Nigeria; on their experience with antegrade and retrograde facial nerve dissection techniques in parotid surgery. The respondents were asked to indicate their choice of dissection techniques in revision parotidectomy; limited superficial parotidectomy; and in obese patients with large tumors. They were also asked to indicate if they routinely used perioperative facial nerve monitoring devices in parotid surgery for benign tumors. Result: About half (47.5) of them routinely used the antegrade technique; while only a few (12.5) used the retrograde technique. A large number of them (40); however; used a combination of antegrade and retrograde routinely. Technical ease was the main reason for the choice of technique. The antegrade technique was the technique of choice by most respondents for revision parotidectomy (60) and limited superficial parotidectomy (62). However; the retrograde approach was the technique of choice by most of them (47) in case of parotidectomy in obese patients with large tumors. The routine use of perioperative facial nerve monitoring devices is an uncommon practice among OMF and ENT surgeons in Nigeria. Conclusions: The antegrade approach for facial nerve dissection is the most common technique used in parotid surgery by Nigerian OMF and ENT surgeons. Nigerian surgeons need to consider the retrograde approach in selected cases of parotid surgery especially for localized tumors that are amenable to limited superficial parotidectomy. Inclusion of perioperative facial nerve monitoring devices is also advocated

Pregnancy Epulis Associated With Life Threatening Haemorrhage in a Nigerian Woman

Pregnancy tumour is a clinical term used to identify a pyogenic granuloma that occurs in pregnant women. Pregnancy tumour is not uncommon; but severe bleeding associated with the lesion necessitating blood transfusion is rare. We report a rare case of mandibular gingival pregnancy tumour with a life-threatening haemorrhage in a 25-year-old Nigerian woman. The patient had lost an estimated 2 litres of blood before presentation. Her packed cell volume was 8at presentation. The patient was managed by infusion of fluid; transfusion of 4 units of blood and ligation of the facial artery; and excision of the lesion. Following an uneventful healing; she was discharged 10 days later with a PCV of 40.5. Following subsequent review there was a recurrence 2 months later that regress after 1 month. She was subsequently lost to further follow up