Natural Continuous Extensions of Runge-Kutta Methods for Volterra Integrodifferential Equations.
R. Vermiglio (1988)
Numerische Mathematik
Burton, T.A. (1991)
Journal of Applied Mathematics and Stochastic Analysis
Wang, Guotao, Zhang, Lihong, Song, Guangxing (2011)
Advances in Difference Equations [electronic only]
Agarwal, Ravi P., Ryoo, Cheon Seoung, Kim, Young-Ho (2007)
Journal of Inequalities and Applications [electronic only]
Heatherly, Henry E., Huffmann, Jason P. (1999)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Žubrinić, Darko (2002)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Hristova, S.G. (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Sikorska-Nowak, Aneta, Nowak, Grzegorz (2007)
International Journal of Mathematics and Mathematical Sciences
Haribhau L. Tidke, Machindra B. Dhakne (2012)
Applications of Mathematics
The aim of the present paper is to investigate the global existence of mild solutions of nonlinear mixed Volterra-Fredholm integrodifferential equations, with nonlocal condition. Our analysis is based on an application of the Leray-Schauder alternative and rely on a priori bounds of solutions.
Chandrasekaran, Mariappan (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Guo, Dajun (1991)
Journal of Applied Mathematics and Stochastic Analysis
Svatopluk Fučík, Dien Hien Tran (1973)
Commentationes Mathematicae Universitatis Carolinae
D. Mangeron, M.N. Oguztöreli, ... (1973)
Monatshefte für Mathematik
Hu, Manfeng, Zhu, Jiang (2004)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Jacques Audounet, Jean-Michel Roquejoffre, Hélène Rouzaud (2002)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.
Jacques Audounet, Jean-Michel Roquejoffre, Hélène Rouzaud (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
This article is devoted to the numerical study of a flame ball model, derived by Joulin, which obeys to a singular integro-differential equation. The numerical scheme that we analyze here, is based upon a one step method, and we are interested in its long-time behaviour. We recover the same dynamics as in the continuous case: quenching, or stabilization of the flame, depending on heat losses, and an energy input parameter.
Batiha, B., Noorani, M.S.M., Hashim, I. (2008)
International Journal of Open Problems in Computer Science and Mathematics. IJOPCM
Dariusz Idczak, A. Skowron, S. Walczak (2014)
Banach Center Publications
We study an integro-differential operator Φ: H̅¹ → L² of Fredholm type and give sufficient conditions for Φ to be a diffeomorphism. An application to functional equations is presented.
Daniela Sforza (1991)
Rendiconti del Seminario Matematico della Università di Padova
Milan Medveď (1978)
Czechoslovak Mathematical Journal