Results 151 to 160 of about 341 (180)

The Numerical Solution of Singular Volterra Integral Equations

SIAM Journal on Numerical Analysis, 1968
It is possible to prove by Laplace transform analysis that (1.1) has a unique solution R(t) satisfying the foregoing conditions. However, this approach is not very useful for numerical purposes. We shall present a practical and efficient method of approximate solution. The successive approximations are piecewise linear.
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On the Solution of a Volterra Integral Equation with a Weakly Singular Kernel

SIAM Journal on Mathematical Analysis, 1973
The solution $x(t)$ of the Volterra integral equation of the second kind $x(t) = f_1 (t) + \sqrt t f_2 (t) + \int _0^t g(t,s,x(s))(t - s)^{ - {1 / 2}} ds$ is examined. It is shown that $x(t) = u(t) + \sqrt t v(t)$, where $u(t)$ and $v(t)$ are smooth under appropriate smoothness conditions on $f_1 (t)$, $f_2 (t)$ and $g(t,s,x)$ and satisfy a system of ...
de Hoog, Frank, Weiss, Richard
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On Volterra Type Singular Integral Equations

Georgian Mathematical Journal, 2001
Conditions for the boundedness are established, and the norms of Volterra type one-dimensional integral operators with fixed singularities of first order in the kernel are calculated in the space L2 with weight. Integral equations of second order, containing the said operators, are investigated.
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Numerical solution of Volterra integral equations with singularities

Frontiers of Mathematics in China, 2013
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Kolk, Marek, Pedas, Arvet
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Superconvergence of Numerical Solutions to Volterra Integral Equations with Singularities

SIAM Journal on Numerical Analysis, 1997
The paper is devoted to the collocation method for weakly singular Volterra integral equations \[ x(t)+ \int^t_0 (t-s)^{-\alpha} h(t,s)x(s)ds= f(t),\quad t\in J=[0,T],\tag{1} \] with ...
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Systems of Fredholm and Volterra Integral Equations: Integrable Singularities

2013
In this chapter we consider three systems of singular integral equations. Specifically we are interested in the following systems of Fredholm integral equations $$\displaystyle{ u_{i}(t) =\int _{ 0}^{1}g_{ i}(t,s)f_{i}(s,u_{1}(s),u_{2}(s),\cdots \,,u_{n}(s))ds,\ \ t \in [0,1],\ 1 \leq i \leq n }$$ (7.1.1) $$\displaystyle{ u_{i}(t) =\int _{
Ravi P. Agarwal, Donal O’Regan, Patricia J. Y. Wong   +2 more
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Parallel methods for weakly singular Volterra integral equations on GPUs

Applied Numerical Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
CONTE, Dajana, PATERNOSTER, Beatrice
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System of nonlinear Volterra’s integral equations with polar kernel and singularities

Nonlinear Analysis: Theory, Methods & Applications, 2007
Using one special Colombeau algebra and the method of regularization of fractional derivatives with a delta sequence, the author proves the existence and the uniqueness of the solution of a system of nonlinear Volterra integral equations with polar kernel.
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Fredholm-Volterra integral equation with singular kernel

Korean Journal of Computational and Applied Mathematics, 1999
The paper deals with the numerical solution of Fredholm-Volterra integral equations with Carleman kernel in the space \(L_2(-1,1)\times C(0,T)\), \(0\leq t\leq ...
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Singular integral equations of volterra type and the finite part of divergent integrals

Archive for Rational Mechanics and Analysis, 1959
of the first and second kind respectively for integral and non-integral values of a ~ t z. In the more,common case 0c 1 an interpretation of the divergent integrals may be sought by CAUCH.Y'S principal values for a ~-t and HADAMARD'S finite parts for a > t.
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