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Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations
Vicente J. BolósRafael Benítezsubject
Non-Lipschitz nonlinearityVolterra integral equationMathematics::Numerical Analysissymbols.namesakeMathematics - Analysis of PDEs45D05 45G10 65R20 34A12Computer Science::Computational Engineering Finance and ScienceCollocation methodFOS: MathematicsOrthogonal collocationNonlinear integral equationsMathematics - Numerical AnalysisUniquenessMathematicsPhysics::Computational PhysicsCollocation methodsCollocationApplied MathematicsMathematical analysisComputer Science::Computation and Language (Computational Linguistics and Natural Language and Speech Processing)Numerical Analysis (math.NA)Nontrivial solutionsIntegral equationComputer Science::Numerical AnalysisNonlinear systemComputational MathematicssymbolsLinear equationAnalysis of PDEs (math.AP)description
We analyze collocation methods for nonlinear homogeneous Volterra-Hammerstein integral equations with non-Lipschitz nonlinearity. We present different kinds of existence and uniqueness of nontrivial collocation solutions and we give conditions for such existence and uniqueness in some cases. Finally we illustrate these methods with an example of a collocation problem, and we give some examples of collocation problems that do not fit in the cases studied previously.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2011-04-01 | Journal of Computational and Applied Mathematics |