The current research attempts to offer a new method for solving fuzzy linear Volterra integral equations system. This method converts the given fuzzy system into a linear system in crisp case by using the Taylor expansion method. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example and also results are...

Taylor expansions of analytic functions are considered with respect to several points, allowing confluence of any of them. Cauchy-type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Lau...

In this paper we intend to offer a numerical scheme to solve linear Fredholm fuzzy integral equations system of the second kind. For this aim, we apply Taylor expansion method to convert the given fuzzy system into linear system in crisp case. Now the solution of this system yields the unknown Taylor coefficients of the solution functions. The proposed method is illustrated by an example. Resul...

a Bk({1− t}) k! f (t)dt where a and b are arbitrary real numbers with difference b − a being a positive integer number, Bn and bn are Bernoulli polynomials and numbers, respectively, and k is any positive integer. The condition we impose on the real function f is that it should have continuous k-th derivative. The symbol {x} for a real number x denotes the fractional part of x. Proof of this th...

Under certain conditions the signature method suggested by Pantiledes and Pryce facilitates the local expansion of DAE solutions by Taylor polynomials of arbitrary order. The successive calculation of Taylor coefficients involves the solution of nonlinear algebraic equations by some variant of the Gauss-Newton method. Hence, one needs to evaluate certain Jacobians and several right hand sides. ...

In this study we produced a new method for solving regular differential equations with step size h and Taylor series. This method analyzes a regular differential equation with initial values and step size h. this types of equations include quadratic and cubic homogenous equations with constant coeffcients and cubic and second-level equations.

We investigate a Maclaurin inequality for vectors and its connection to an Aleksandrov-type parallelepipeds.

Abstract. We compare, in the multidimensional case, the Fourier integral of a function λ of bounded variation and the corresponding trigonometric series with the coefficients λ(k). Posing additional smoothness conditions on the function, we infer that the difference between the two mentioned values is controlled not only by the total variation as in dimension one and by certain multivariate ver...

In this work we provide a step by derivation of an angular--averaged Ewald potential suitable for numerical simulations disordered Coulomb systems. The was first introduced E.\,Yakub and C.\,Ronchi without clear derivation. Two methods are used to find the coefficients series expansion potential: based on Euler--Maclaurin Poisson summation formulas. expressions each coefficient is represented a...