in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

substantiation of the averaging method for differential equations with maxima is presented. two theorems on substantiates for differential equations with maxima are established.

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.

in this article differential transformation method (dtms) has been used to solve neutral functional-differential equations with proportional delays. the method can simply be applied to many linear and nonlinear problems and is capable of reducing the size of computational work while still providing the series solution with fast convergence rate. exact solutions can also be obtained from the kno...

‎the main purpose of this paper is to study the numerical solution of nonlinear volterra integral equations with constant delays, based on the multistep collocation method. these methods for approximating the solution in each subinterval are obtained by fixed number of previous steps and fixed number of collocation points in current and next subintervals. also, we analyze the convergence of the...

in this paper, we will present a review of the multistep collocation method for delay volterra integral equations (dvies) from [1] and then, we study the superconvergence analysis of the multistep collocation method for dvies. some numerical examples are given to confirm our theoretical results.