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Itô Differential Representation of Singular Stochastic Volterra Integral Equations
Acta Mathematica Scientia, 2020 12 ...
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Numerical Solution of a Free Boundary Problem from Heat Transfer by the Second Kind Chebyshev Wavelets [PDF]
Journal of Sciences, Islamic Republic of Iran, 2019 In this paper we reduce a free boundary problem from heat transfer to a weakly Singular Volterra integral equation of the first kind. Since the first kind integral equation is ill posed, and an appropriate method for such ill posed problems is based on ...
Bahman Babayar-Razlighi
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Local time and the pricing of time-dependent barrier options [PDF]
, 2008 A time-dependent double-barrier option is a derivative security that delivers the terminal value $\phi(S_T)$ at expiry $T$ if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval $[0,T]$. Using a
A. Friedman +36 more
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A Singular Nonlinear Volterra Integral Equation
Journal of Integral Equations and Applications, 1993 Many problems in Applied Mathematics lead to the study of the nonlinear partial differential equation \(u_ t = (a(u))_{xx} + (b(u))_ x + c(u)\). The interest in the existence of travelling-wave solutions of the form \(U(x,t) = U(\psi)\), \(\psi = x - \lambda t\), originates an ordinary differential equation from which arise integral equations of the ...
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, 2017 For kernels $\nu$ which are positive and integrable we show that the operator $g\mapsto J_\nu g=\int_0^x \nu(x-s)g(s)ds$ on a finite time interval enjoys a regularizing effect when applied to H\"older continuous and Lebesgue functions and a "contractive"
Adami +39 more
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Exponential stabilization of volterra integral equations with singular kernels
Journal of Integral Equations and Applications, 1988 Stabilization problems for certain problems of partial-differential integral equations with possible singular kernels as encountered in the theory of linear viscoelasticity are discussed. Applications of the theory to some mechanical stabilization problems are also illustrated.
Desch, Wolfgang, Miller, Richard K.
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Journal of Function Spaces, 2017 We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-
Haotao Cai
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Solving one pseudo-Volterra integral equation
Қарағанды университетінің хабаршысы. Математика сериясы, 2019 In this paper, we study the solvability of a second - kind pseudo-Volterra integral equation. By replacing the right - hand side and the unknown function, the integral equation is reduced to an integral equation, the kernel of which is not «compressible»
M.T. Kosmakova +4 more
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Extrapolation Method for Non-Linear Weakly Singular Volterra Integral Equation with Time Delay
Mathematics, 2021 This paper proposes an extrapolation method to solve a class of non-linear weakly singular kernel Volterra integral equations with vanishing delay. After the existence and uniqueness of the solution to the original equation are proved, we combine an ...
Li Zhang, Jin Huang, Hu Li, Yifei Wang
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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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