On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations

المؤلفون المشاركون

Dlamini, P. G.
Khumalo, Melusi

المصدر

Mathematical Problems in Engineering

العدد

المجلد 2012، العدد 2012 (31 ديسمبر/كانون الأول 2012)، ص ص. 1-11، 11ص.

الناشر

Hindawi Publishing Corporation

تاريخ النشر

2012-05-20

دولة النشر

مصر

عدد الصفحات

11

التخصصات الرئيسية

هندسة مدنية

الملخص EN

We make use of an adaptive numerical method to compute blow-up solutions for nonlinear ordinary Volterra integrodifferential equations (VIDEs).

The method is based on the implicit midpoint method and the implicit Euler method and is named the implicit midpoint-implicit Euler (IMIE) method and was used to compute blow-up solutions in semilinear ODEs and parabolic PDEs in our earlier work.

We demonstrate that the method produces superior results to the adaptive PECE-implicit Euler (PECE-IE) method and the MATLAB solver of comparable order just as it did in our previous contribution.

We use quadrature rules to approximate the integral in the VIDE and demonstrate that the choice of quadrature rule has a significant effect on the blow-up time computed.

In cases where the problem contains a convolution kernel with a singularity we use convolution quadrature.

نمط استشهاد جمعية علماء النفس الأمريكية (APA)

Dlamini, P. G.& Khumalo, Melusi. 2012. On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations. Mathematical Problems in Engineering،Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-1002051

نمط استشهاد الجمعية الأمريكية للغات الحديثة (MLA)

Dlamini, P. G.& Khumalo, Melusi. On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations. Mathematical Problems in Engineering No. 2012 (2012), pp.1-11.
https://search.emarefa.net/detail/BIM-1002051

نمط استشهاد الجمعية الطبية الأمريكية (AMA)

Dlamini, P. G.& Khumalo, Melusi. On the Computation of Blow-Up Solutions for Nonlinear Volterra Integrodifferential Equations. Mathematical Problems in Engineering. 2012. Vol. 2012, no. 2012, pp.1-11.
https://search.emarefa.net/detail/BIM-1002051

نوع البيانات

مقالات

لغة النص

الإنجليزية

الملاحظات

Includes bibliographical references

رقم السجل

BIM-1002051