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RESEARCH PRODUCT

Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations

Rafael BenítezVicente J. Bolós

subject

CollocationApplied MathematicsMathematical analysisMathematics::Analysis of PDEsComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Numerical Analysis (math.NA)Volterra integral equationIntegral equationMathematics::Numerical AnalysisComputational MathematicsNonlinear systemsymbols.namesakeMathematics - Analysis of PDEs45D05 45G10 65R20 34A12HomogeneousComputer Science::Computational Engineering Finance and ScienceCollocation methodFOS: MathematicssymbolsOrthogonal collocationUniquenessMathematics - Numerical AnalysisAnalysis of PDEs (math.AP)Mathematics

description

In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.

yearjournalcountryeditionlanguage
2011-12-20
10.1016/j.amc.2015.01.057http://arxiv.org/abs/1112.4658