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Khajehnasiri, Amirahmad, Safavi, Mostafa, Banar, Jalal. (1399). Application of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation. پژوهشنامه مدیریت اجرایی, 9(2), 321-339. doi: 10.22080/cjms.2019.17199.1421
Amirahmad Khajehnasiri; Mostafa Safavi; Jalal Banar. "Application of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation". پژوهشنامه مدیریت اجرایی, 9, 2, 1399, 321-339. doi: 10.22080/cjms.2019.17199.1421
Khajehnasiri, Amirahmad, Safavi, Mostafa, Banar, Jalal. (1399). 'Application of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation', پژوهشنامه مدیریت اجرایی, 9(2), pp. 321-339. doi: 10.22080/cjms.2019.17199.1421
Khajehnasiri, Amirahmad, Safavi, Mostafa, Banar, Jalal. Application of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation. پژوهشنامه مدیریت اجرایی, 1399; 9(2): 321-339. doi: 10.22080/cjms.2019.17199.1421

Application of Legendre operational matrix to solution of two dimensional nonlinear Volterra integro-differential equation

Caspian Journal of Mathematical Sciences
مقاله 14، دوره 9، شماره 2، آذر 2020، صفحه 321-339    اصل مقاله (458.74 K)
نوع مقاله: Research Articles
شناسه دیجیتال (DOI): 10.22080/cjms.2019.17199.1421
نویسندگان
Amirahmad Khajehnasiri* 1؛ Mostafa Safavi2؛ Jalal Banar3
1Department of Mathematics, North Tehran Branch, Islamic Azad University, Tehran, Iran
2Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran
3Department of Mathematics, Firoozkooh Branch,\ Islamic Azad University, Firoozkooh, Iran
تاریخ دریافت: 01 مهر 1398،  تاریخ بازنگری: 25 آبان 1398،  تاریخ پذیرش: 04 آذر 1398 
چکیده
In this article, we apply the operational matrix to find the numerical solution of two- dimensional nonlinear Volterra integro-differential equation (2DNVIDE). Form this prospect, two-dimensional shifted Legendre functions (2DSLFs) has been presented for integration, product as well as differentiation. This method converts 2DNVIDE to an algebraic system of equations, so the numerical solution of 2DNVIDE is computable. The effectiveness and accuracy of the method were examined with some examples as well. The results and comparison with other methods have shown a remarkable performance.
کلیدواژه‌ها
Volterra integro-differential equation؛ Two-dimensional Legendre polynomials؛ Operational matrix؛ Error estimation
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