Numerical Solution of Integral Equations, Fast Algorithms and Krein-Sobolev Equation.
Numerical Solution of Integral Equations in Chebyshev Series.
Numerical solution of integral equations with finite part integrals.
Numerical solution of the second kind singular Volterra integral equations by modified Navot-Simpson's quadrature.
Numerical Solution of Volterra Integral Equation.
Numerical Solution of Volterra Integral Equations.
Numerical solutions for second-kind Volterra integral equations by Galerkin methods
In this paper, we study the global convergence for the numerical solutions of nonlinear Volterra integral equations of the second kind by means of Galerkin finite element methods. Global superconvergence properties are discussed by iterated finite element methods and interpolated finite element methods. Local superconvergence and iterative correction schemes are also considered by iterated finite element methods. We improve the corresponding results obtained by collocation methods in the recent...
Numerical Solutions of Integral Equations on the Half Line. I. The Compact Case.
Numerical solutions of the nonlinear integro-differential equations.
Numerical solutions of third kind integral-algebraic equations
Numerical solutions to integral equations equivalent to differential equations with fractional time
This paper presents an approximate method of solving the fractional (in the time variable) equation which describes the processes lying between heat and wave behavior. The approximation consists in the application of a finite subspace of an infinite basis in the time variable (Galerkin method) and discretization in space variables. In the final step, a large-scale system of linear equations with a non-symmetric matrix is solved with the use of the iterative GMRES method.
Numerical solvability of a class of Volterra-Hammerstein integral equations with noncompact kernels.
Numerical treatment of a time dependent inverse problem in photon transport
The time-dependent intensity of a UV-photon source, located inside an interstellar cloud, is determined by formulating and solving an inverse problem for the integro-differential transport equation of photons in a one-dimensional slab. Starting from a discretizazion of the forward problem, an iterative procedure is used to compute the values of the source intensity at increasing values of the time.
Numerical treatment of fixed point applied to the nonlinear Fredholm integral equation.
Numerical Treatment of Singular Integral Equations by Interpolation Methods.
On a contact problem for a viscoelastic von Kármán plate and its semidiscretization
We deal with the system describing moderately large deflections of thin viscoelastic plates with an inner obstacle. In the case of a long memory the system consists of an integro-differential 4th order variational inequality for the deflection and an equation with a biharmonic left-hand side and an integro-differential right-hand side for the Airy stress function. The existence of a solution in a special case of the Dirichlet-Prony series is verified by transforming the problem into a sequence of...
On a reliable solution of a Volterra integral equation in a Hilbert space
We consider a class of Volterra-type integral equations in a Hilbert space. The operators of the equation considered appear as time-dependent functions with values in the space of linear continuous operators mapping the Hilbert space into its dual. We are looking for maximal values of cost functionals with respect to the admissible set of operators. The existence of a solution in the continuous and the discretized form is verified. The convergence analysis is performed. The results are applied to...
On approximate solutions of initial value problems for integro-differential equation with quasilinear differential operator and generalized Volterra operator
On Bateman's Method for Second Kind Integral Equations.
On convergence of quadrature-differences method for linear singular integro-differential equations on the interval
Here we propose and justify the quadrature-differences method for the full linear singular integro-differential equations with Cauchy kernel on the interval . We consider equations of zero, positive and negative indices. It is shown, that the method converges to exact solution and the error estimate depends on the sharpness of derivative approximation and the smoothness of the coefficients and the right-hand side of the equation.