in this article,we present a wavelet method for solving stochastic volterra integral equations based on haar wavelets. first, we approximate all functions involved in the problem by haar wavelets then, by substituting the obtained approximations in the problem, using the it^{o} integral formula and collocation points then, the main problem changes into a system of linear or nonlinear equation w...

An algorithm is provided for the fast and accurate computation of the solution of nonhomogeneous Cauchy-Riemann equations in the complex plane in the interior of a unit disk. The algorithm is based on the representation of the solution in terms of a double integral, some recursive relations in Fourier space, and fast Fourier transforms. The numerical evaluation of the solution at N2 points on a...

We construct new families of (q-) difference and (contour) integral operators having nice actions on Koornwinder’s multivariate orthogonal polynomials. We further show that the Koornwinder polynomials can be constructed by suitable sequences of these operators applied to the constant polynomial 1, giving the difference-integral representation of the title. Macdonald’s conjectures (as proved by ...

n this paper, we apply Picard’s Iteration Method followed by Adomian Decomposition Method to solve a nonlinear Singular Cauchy Problem of Euler- Poisson- Darboux Equation. The solution of the problem is much simplified and shorter to arriving at the solution as compared to the technique applied by Carroll and Showalter (1976)in the solution of Singular Cauchy Problem. 

* Correspondence: baak@hanyang. ac.kr Department of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, South Korea Full list of author information is available at the end of the article Abstract Using the fixed point method, we prove the Hyers-Ulam stability of a Cauchy-Jensen type additive set-valued functional equation, a Jensen type additive-quadratic se...

We state mean ergodic theorems with rates of approximation for a new class of operator families. Our result provides a unified approach to convergence rates for many particular strongly continuous solution families associated to linear evolution equations such as the abstract Cauchy problem of the first and second order, and integral Volterra equations of convolution type. We discuss in particu...

A nonlinear stochastic integral equation of the Hammerstein type in the form x(t; c) = h(t; co) + f k(t, s; co)f (s, x(s; co)) dy (s) is studied where t E S, a v-finite measure space with certain properties, co E Q, the supporting set of a probability measure space (Q, A, P), and the integral is a Bochner integral. A random solution of the equation is defined to be a second order vector-valued ...

The paper contains a systematic presentation of how the so-called “W-transform” can be used to study stability of stochastic functional differential equations. The W-transform is an integral transform which typically is generated by a simpler differential equation (“reference equation”) via the Cauchy representation of its solutions (“variation-of-constant formula”). This other equation is supp...

An alternative approach is proposed here to investigate the problem of scattering surface water waves by a vertical permeable plate submerged in deep within framework linear wave theory. Using Havelock’s expansion potential, associated boundary value reduced second kind hypersingular integral equation order 2. The unknown function expressed as product suitable weight and an polynomial. 2 evalua...