Results 21 to 30 of about 9,176 (267)
On fully discrete collocation methods for solving weakly singular integral equations
Mathematical Modelling and Analysis, 2009 A popular class of methods for solving weakly singular integral equations is the class of piecewise polynomial collocation methods. In order to implement those methods one has to compute exactly certain integrals that determine the linear system to be ...
Raul Kangro, Inga Kangro
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On integral equations with Weakly Singular kernel by using Taylor series and Legendre polynomials
Open Physics, 2015 This paper is concerned with the numerical solution for a class of weakly singular Fredholm integral equations of the second kind. The Taylor series of the unknown function, is used to remove the singularity and the truncated Taylor series to second ...
Babolian Esmail +4 more
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Multiresolution separated representations of singular and weakly singular operators
Applied and Computational Harmonic Analysis, 2007 For a finite but arbitrary precision, efficient low separation rank representations for the Poisson kernel and for the projector on the divergence free functions in the dimension \(d=3\)are constructed. The given construction requires computing only one-dimensional integrals.
Beylkin, Gregory +3 more
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On the Volterra integral equation with weakly singular kernel [PDF]
Mathematica Bohemica, 2006 Summary: We give sufficient conditions for the existence of at least one integrable solution of equation \(x(t)=f(t)+\int _{0}^{t} K(t,s)g(s,x(s))\,ds\). Our assumptions and proofs are expressed in terms of measures of noncompactness.
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A Class of Iterative Nonlinear Difference Inequality with Weakly Singularity [PDF]
Journal of Applied Mathematics, 2014 We discuss a class of new nonlinear weakly singular difference inequality, which is solved by change of variable, discrete Hölder inequality, discrete Jensen inequality, the mean-value theorem for integrals and amplification method, and Gamma function. Explicit bound for the unknown function is given clearly.
Chunmiao Huang +2 more
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Mathematical Modelling and Analysis, 2008 Piecewise polynomial collocation methods on special nonuniform grids are efficient methods for solving weakly singular Fredholm and Volterra integral equations but there is a widespread belief that those methods are numerically unstable in the case of ...
Raul Kangro, Inga Kangro
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The predictability of large-scale wind-driven flows [PDF]
Nonlinear Processes in Geophysics, 2001 The singular values associated with optimally growing perturbations to stationary and time-dependent solutions for the general circulation in an ocean basin provide a measure of the rate at which solutions with nearby initial conditions begin to ...
A. Mahadevan +4 more
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Reconstructing enzyme evolution by protein engineering
FEBS Letters, EarlyView.Natural enzyme evolution can be retraced by protein engineering methods such as directed evolution, rational design, and ancestral sequence reconstruction. These approaches reveal how enzymes emerged from ligand‐binding scaffolds, developed varying substrate preferences, formed oligomeric complexes, adapted to environmental changes, and evolved novel ...
Lukas Drexler +2 more
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Mathematical Modelling and AnalysisFor Volterra integro-differential equations (VIDEs) with weakly singular kernels, their solutions are singular at the initial time. This property brings a great challenge to traditional numerical methods. Here, we investigate the numerical approximation
ZhiPeng Liu, DongYa Tao, Chao Zhang
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Integrable Singularities and Weakly Sequentially Continuous Maps
Zeitschrift für Analysis und ihre Anwendungen, 2003 New existence results for singular second order boundary value problems, where the singularity is integrable, are presented using fixed point theory for weakly sequentially continuous maps.
Agarwal, R. P., O'Regan, D.
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