Search results for "Orthogonal collocation"

showing 3 items of 3 documents

Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations

2011

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.

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
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Existence and uniqueness of nontrivial collocation solutions of implicitly linear homogeneous Volterra integral equations

2011

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.

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)Journal of Computational and Applied Mathematics
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Exponential convergence andH-c multiquadric collocation method for partial differential equations

2003

The radial basis function (RBF) collocation method uses global shape functions to interpolate and collocatethe approximate solution of PDEs. It is a truly meshless method as compared to some of the so-calledmeshless or element-free finite element methods. For the multiquadric and Gaussian RBFs, there are twoways to make the solution converge—either by refining the mesh size

Numerical AnalysisRegularized meshless methodPartial differential equationApplied MathematicsGaussianMathematical analysisResidualSingular boundary methodComputational Mathematicssymbols.namesakeCollocation methodsymbolsOrthogonal collocationRadial basis functionAnalysisMathematicsNumerical Methods for Partial Differential Equations
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