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DEVIATION OF THE ERROR ESTIMATION FOR VOLTERRA INTEGRO-DIFFERENTIAL EQUATIONS

Acta Mathematica Scientia 2018年第4期38卷 1322-1344页

作者： Mohammad ZAREBNIA Reza PARVAZ amir saboor bagherzadeh Department of Mathematics University of Mohaghegh Ardabili Department of Applied Mathematics Faculty of Mathematics Ferdowsi University of Mashhad

In this paper, we study an efficient asymptotically correction of a-posteriori er- ror estimator for the numerical approximation of Volterra integro-differential equations by piecewise polynomial collocation method. The deviation of the error for Volterra integro- differential equations by using the defect correction principle is defined. Also, it is shown that for m degree piecewise polynomial collocation method, our method provides O（hm＋l） as the order of the deviation of the error. The theoretical behavior is tested on examples and it is shown that the numerical results confirm the theoretical part.

关键词： Volterra integro-differential defect correction principle piecewise polynomial collocation finite difference error analysis

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Low gradient ascites: A seven-year course review

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World Journal of Gastroenterology 2005年第15期11卷 2337-2339页

作者： Fariborz Mansour-Ghanaei Afshin Shafaghi amir-Hossein bagherzadeh Mohammad-Sadegh Fallah Gastrointestinal and Liver Diseases Research Center (GLDRC)

AIM: To study the patients with low gradient ascites in hospitals of Guilan Province (northern Iran).METHODS: Patients admitted in hospitals of Guilan Province with low gradient ascites from 1993 to 2000 were enrolled in the study. Serum and ascitic fluid albumin levels were determined by biochemical reactions. The serum-ascitic albumin gradient (SAAG) less than 1.1 g/dL was considered low. Statistical analysis was performed with SPSS 9.0software and P＜0.05 was considered statistically ***: Of the 148 patients enrolled in the study, 72(48.6%) were males and 76 (51.4%) were females with a mean age of 59.03±13.54 years. Tuberculous peritonitis was the most frequent cause of low gradient ascites in 68 (45.9%). Other most frequent causes were cancer in 62 (41.9%), nephrotic syndrome in 9 (6%), pancreatitis in 6 (4%). Peritoneal cancer was found in 22 (35%),ovarian and gastric cancers were found in 14 (22.5%)and 12 (19.3%), respectively. All of which were the causes of ascites. The mean SAAG was 0.68±0.19 g/dL. The mean serum and ascitic fluid albumin concentrations were higher in tuberculous patients (P＜0.006), but lactate dehydrogenase (LDH) level was higher in cancer patients (P＜0.0001). In peritoneal tuberculosis, mean ascitic glucose concentration was significantly lower than other patients (P＜0.0001).CONCLUSION: Tuberculosis should be considered in all patients with low gradient ascites especially in developing countries (like Iran), as the first cause of ascites. In the approach to patients with low gradient ascites, ascitic fluid glucose, and LDH level are useful indicators for decision making.

关键词： Ascites Tuberculosis Cancer Albumin

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