The first passage time problem for Brownian motions hitting a barrier has been extensively studied in the literature. In particular, many incarnations of integral equations which link the density of the hitting time to the equation for the barrier itself have appeared. Most interestingly, Peskir (2002b) demonstrates that a master integral equation can be used to generate a countable number of n...

Direct inversion of acoustic scattering problems is nonlinear. One way to treat the inverse scattering problem is based on the reversion of the Born–Neumann series solution of the Lippmann–Schwinger equation. An important issue for this approach is the radius of convergence of the Born–Neumann series for the forward problem. However, this issue can be tackled by employing a renormalization tech...

In this paper, an efficient method is presented for solving two dimensional Fredholm and Volterra integral equations of the second kind. Chebyshev polynomials are applied to approximate a solution for these integral equations. This method transforms the integral equation to algebraic equations with unknown Chebyshev coefficients. The high accuracy of this method is verified through some numeric...

We apply Mönch type fixed point theorems for acyclic multivalued maps to the solvability of inclusions of Hammerstein type in Banach spaces. Our approach makes possible to unify and improve the existence theories for nonlinear evolution problems and abstract integral inclusions of Volterra and Fredholm type.

in this letter, the numerical scheme of nonlinear volterra-fredholm integro-differential equations is proposed in a reproducing kernel hilbert space (rkhs). the method is constructed based on the reproducing kernel properties in which the initial condition of the problem is satised. the nonlinear terms are replaced by its taylor series. in this technique, the nonlinear volterra-fredholm integr...

In this paper, we study the existence of solutions of some nonlinear Volterra integral equations by using the techniques of measures of noncompactness and the Petryshyn's fixed point theorem in Banach space. We also present some examples of the integral equation to confirm the efficiency of our results.

Abstract: We study the numerical solvability of a class of nonlinear Volterra-Fredholm integral equations. We obtain existence and uniqueness results and analyze the linearization methods for these equations under some verifiable conditions on the kernels and nonlinear functions. Also, linearazation methods for initial value problems which have singular points are introduced. The stability esti...

Homotopy Analysis Method (HAM) and Homotopy Perturbation Method (HPM) are two analytic methods to solve the linear and nonlinear equations which can be used to obtain the numerical solution. This paper presents the application of the HAM to Fredholm and Volterra integral equations. The HAM contains the auxiliary parameter ~, that provides a powerful tool to analyze strongly linear and nonlinear...

In 1982, Dubois and Prade [4, 5] first introduced the concept of integration of fuzzy functions. Kaleva [7] studied the measurability and integrability for the fuzzy set-valued mappings of a real variable whose values are normal, convex, upper semicontinuous, and compactly supported by fuzzy sets in Rn. Existence of solutions of fuzzy integral equations has been studied by several authors [1, 2...