The method of successive approximation for functional equations

A Novel Successive Approximation Method for Solving a Class of Optimal Control Problems

This paper presents a successive approximation method (SAM) for solving a large class of optimal control problems. The proposed analytical-approximate method, successively solves the Two-Point Boundary Value Problem (TPBVP), obtained from the Pontryagin's Maximum Principle (PMP). The convergence of this method is proved and a control design algorithm with low computational complexity is present...

Degenerate kernel approximation method for solving Hammerstein system of Fredholm integral equations of the second kind

Degenerate kernel approximation method is generalized to solve Hammerstein system of Fredholm integral equations of the second kind. This method approximates the system of integral equations by constructing degenerate kernel approximations and then the problem is reduced to the solution of a system of algebraic equations. Convergence analysis is investigated and on some test problems, the propo...

A Successive Minima Method for Implicit Approximation

This paper is concerned with the problem of approximating a collection of unorganized data points by an algebraic tensor-product B-spline curve. The implicit approximation to data points would be ideally based on minimizing the sum of squares of geometric distance. Since the geometric distance from a point to an implicit curve cannot be computed analytically, Sampson distance, which is the firs...

The Taylor Method for Numerical Solution of Fuzzy Generalized Pantograph Equations with Linear Functional Argument

An efficient method for the numerical solution of functional integral equations

We propose an efficient mesh-less method for functional integral equations. Its convergence analysis has been provided. It is tested via a few numerical experiments which show the efficiency and applicability of the proposed method. Attractive numerical results have been obtained.