Results 81 to 90 of about 121 (115)
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On the Numerical Solution of Hypersingular and Singular Integral Equations on the Circle
Differential Equations, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lifanov, I. K., Poltavskij, L. N.
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On the Solvability of a Hypersingular Integral Equation on a Surface with Isothermal Coordinates
Differential Equations, 2021zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Numerical integration schemes for the BEM solution of hypersingular integral equations
International Journal for Numerical Methods in Engineering, 1999Summary: We consider singular and hypersingular integral equations associated with 2D boundary value problems defined on domains whose boundaries have piecewise smooth parametric representations. In particular, given any (polynomial) local basis, we show how to compute efficiently all integrals required by the Galerkin method.
AIMI A. +2 more
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Complex hypersingular integrals and integral equations in plane elasticity
Acta Mechanica, 1994Complex hypersingular (finite-part) integrals and integral equations are considered in the functional class of Muskhelishvili. The appropriate definition is given. Three regularization (equivalence) formulae follow from this definition. They reduce hypersingular integrals to singular ones and allow to derive hypersingular analogues for Sokhotsky ...
Linkov, A. M., Mogilevskaya, S. G.
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Iterative Substructuring for Hypersingular Integral Equations in $\Bbb R^3$
SIAM Journal on Scientific Computing, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Heuer, Norbert, Stephan, Ernst P.
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Approximate Solutions of a Hypersingular Boundary Integral Equation
2009 Second International Conference on Information and Computing Science, 2009In the paper, a reproducing kernel method of solving hypersingular integral equations (HSIE) with cosecant kernel is proposed. Difficulties lie in its singular term of solving HSIE. In order to remove singular term, hypersingular term with square cosecant kernel is transformed into singular term with Hilbert kernel. Subsequently, by making a equivalent
Lihua Mu, Hong Du, Jihong Shen
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On the Numerical Solution of a Hypersingular Integral Equation with Fixed Singularities
2008For the numerical solution of the hypersingular integral equation of a notched half-plane problem we propose collocation methods which look for an approximation of the derivative of the solution of the original equation. This derivative is the solution of a Cauchy singular integral equation with additional fixed singularities.
M. R. CAPOBIANCO +2 more
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PARABOLIC PSEUDODIFFERENTIAL EQUATIONS, HYPERSINGULAR INTEGRALS, AND MARKOV PROCESSES
Mathematics of the USSR-Izvestiya, 1989The author constructs and investigates the fundamental solution of the following Cauchy problem \[ \partial u(x,t)/\partial t+(Au)(x,t)+\sum^{m}_{k=1}(A_ ku)(x,t)=f(x,t),\quad x\in R^ n,\quad t\in (0,T];\quad u(x,0)=\phi (x). \] Here \(A,A_ 1,...,A_ m\) are pseudodifferential operators with symbols \(a(x,t,\xi),a_ 1(x,t,\xi),...,a_ m(x,t,\xi ...
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The numerical treatment of hypersingular integral equations
2000The authors formulate convergence results for collocation and discrete collocation methods for integro-differential equations of Prandtl's type in weighted Sobolev spaces and in weighted spaces of continuous functions. Numerical experiments for two equations confirm the predicted convergence rates.
M. R. CAPOBIANCO, CRISCUOLO, GIULIANA
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Approximate Methods for Solving Hypersingular Integral Equations
2021The work is devoted to a review of analytical and numerical methods for solving linear hypersingular integral equations. Hypersingular integral equations of the first and second kind on closed and open integration intervals are considered. Particular attention is paid to equations with second-order singularities, since these equations are most in ...
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