stefan problem with kinetics is reduced to a system of nonlinear volterra integral equations of second kind and newton's method is applied to linearize it. product integration solution of the linear form is found and sufficient conditions for convergence of the numerical method are given. an example is provided to illustrated the applicability of the method.

The inverse problem of finding the coefficient γ in the equation u̇ = A(t)u + γ(t)u + f(t) from the extra data of the form φ(t) = 〈u(t), w〉 is studied. The problem is reduced to a Volterra equation of the second kind. Applications are given to parabolic equations with second order differential operators.

Many problems of computational electromagnetics [1,2], stationary heat transfer [3,4] and elasticity theory [5] can be naturally reduced to integral equations of the first kind (IEFK) with a weak singularity. So we shall name the equations with a logarithmic peculiarity in one-dimensional case and equation with a peculiarity of an aspect 1 0 rMM in two-dimensional case, where rMM 0 is distance ...

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

The main purpose of this work is to provide a novel numerical approach for the Volterra integral equations based on a spectral approach. A Legendre-collocation method is proposed to solve the Volterra integral equations of the second kind. We provide a rigorous error analysis for the proposed method, which indicates that the numerical errors decay exponentially provided that the kernel function...

In this paper, by using the theories and methods of integral equation and computer algebra, a reliable algorithm for solving the Volterra integral equation is established, and a new Maple algorithm mainproc is established, too. Some examples are presented to illustrate the implementations of the algorithm. The results of the examples indicate that the algorithm of Taylor polynomial method is si...