A simple method for solving Prandtl's integro-differential equation is proposed based on a new reproducing kernel space. Using a transformation and modifying the traditional reproducing kernel method, the singular term is removed and the analytical representation of the exact solution is obtained in the form of series in the new reproducing kernel space. Compared with known investigations, its ...

we are concerned with the development of a k−step method for the numerical solution of fuzzy initial value problems. convergence and stability of the method are also proved in detail. moreover, a specific method of order 4 is found. the numerical results show that the proposed fourth order method is efficient for solving fuzzy differential equations.

‎in this paper we introduce a numerical approach that solves optimal control problems (ocps)‎‎using collocation methods‎. ‎this approach is based upon b-spline functions‎.‎the derivative matrices between any two families of b-spline functions are utilized to‎‎reduce the solution of ocps to the solution of nonlinear optimization problems‎.‎numerical experiments confirm our theoretical findings‎.

in this work, the solution of a boundary value problem is discussed via asemi analytical method. the purpose of the present paper is to inspect theapplication of the adomian decomposition method for solving the nagumotelegraph equation. the numerical solution is obtained for some special casesso that demonstrate the validity of method.

the main attempt of this article is extension the method so that it generallywould be able to consider the classical solution of the systems and moreover,produces the optimal trajectory and control directly at the same time. there-fore we consider a control system governed by a bone marrow cancer equation.next, by extending the underlying space, the existence of the solution is con-sidered and ...

‎a numerical technique based on the collocation method using legendre multiwavelets are‎‎presented for the solution of forced duffing equation‎. ‎the operational matrix of integration for‎‎legendre multiwavelets is presented and is utilized to reduce the solution of duffing equation‎‎to the solution of linear algebraic equations‎. ‎illustrative examples are included to demonstrate‎‎the validity...

‎the global fom and gmres algorithms are among the effective‎ ‎methods to solve sylvester matrix equations‎. ‎in this paper‎, ‎we‎ ‎study these algorithms in the case that the coefficient matrices‎ ‎are real symmetric (real symmetric positive definite) and extract‎ ‎two cg-type algorithms for solving generalized sylvester matrix‎ ‎equations‎. ‎the proposed methods are iterative projection metho...

in this paper, we demonstrate the existence and uniqueness a semianalytical solution of an inverse heat conduction problem (ihcp) in the form: ut = uxx in the domain d = {(x, t)| 0 < x < 1, 0 < t t}, u(x, t) = f(x), u(0, t) = g(t), and ux(0, t) = p(t), for any 0 t t. some numerical experiments are given in the final section.