in this paper, a nonlinear volterra-fredholm integral equation of the first kind is solved by using the homotopy analysis method (ham). in this case, the first kind integral equation can be reduced to the second kind integral equation which can be solved by ham. the approximate solution of this equation is calculated in the form of a series which its components are computed easily. the accuracy...

in this paper, an iterative scheme for extracting approximate solutions of two dimensional volterra-fredholm integral equations is proposed. considering some conditions on the kernel of the integral equation obtained by discretization of the integral equation, the convergence of the approximate solution to the exact solution is investigated. several examples are provided to demonstrate the effc...

in this paper, we present a method for solving the rst kind abel integral equation. in thismethod, the rst kind abel integral equation is transformed to the second kind volterraintegral equation with a continuous kernel and a smooth deriving term expressed by weaklysingular integrals. by using sidi's sinm - transformation and modi ed navot-simpson'sintegration rule, an algorithm for...

We extend the definition of Walsh’s martingale measure stochastic integral so as to be able to solve stochastic partial differential equations whose Green’s function is not a function but a Schwartz distribution. This is the case for the wave equation in dimensions greater than two. Even when the integrand is a distribution, the value of our stochastic integral process is a real-valued martinga...

in this paper, existence theorems for the fuzzy volterra-fredholm integral equations of mixed type (fvfiemt) involving fuzzy number valued mappings have been investigated. then, by using banach's contraction principle, sufficient conditions for the existence of a unique solution of fvfiemt are given. finally, illustrative examples are presented to validate the obtained results.

We present computational results using CORAL, a parallel, three-dimensional, nonlinear magnetostatic code based on a volume integral equation formulation. A key feature of CORAL is the ability to solve, in parallel, the large, dense systems of linear equations that are inherent in the use of integral equation methods. Using the Chameleon and PSLES libraries ensures portability and access to the...

The monodromy operator of a linear delay differential equation with periodic coefficients is formulated as an integral operator. The kernel of this operator includes a factor formed from the fundamental solution of the linear delay differential equation. Although the properties of the fundamental solutions are known, in general there is no closed form for the fundamental solution. This paper de...