methods are iterative: we start with an initial guess x0 of the solution, ... which is called the method of successive approximation (or substitution).
Successive approximation methods for the solution of optimal control problems 137 is minimised, subject to the constraints dx dt = fix(t), u(t), t'] ; X(to) = c (2) G[x(t $), t f] =0 (3) Here x(t)eE n, u(t)eE m, fis a function mapping E n+m+ 1 toe n and G is a function mapping E n+t to E r, p<_n.The time tf may be explicitly or implicitly specified.
Different types of analytical methods and numerical methods were used to solve the problem [1]-[36]. In this article we have applied the successive ap-proximation method used by using the Maple algorithm by applying this algo-rithm to different examples, including finding the approximate solution and
The method of successive approximations constitutes a so-called “algorithmor algorithmic process” for solving equations of a certain class in terms of a ...
Are there any differences between a method of successive approximation and Picard method of successive approximation. ... Browse other questions tagged ordinary-differential-equations numerical-methods or ask your own question. Featured on Meta ...
This method of successive approximation is a basic tool of calculus. It ... you will be able to solve a vast array of problems that other methods can't.
numerical results, the method of successive approximations (MSA) is used. ... applied in [10-13] to the calculation of thin bending plates in the form that ...
Further analysis showed that the successive approximation method solution is ... Therefore, numerical methods must be used to predict acoustic streaming in ...
This paper presents two methods for approximating the solution of a Fredholm integral equation, using the successive approximations method with the ...
In this paper, we will use the successive approximation method for solving Fredholm integral equation of the second kind using Maple18. By means of this method, an algorithm is successfully established for solving the non-linear Fredholm integral equation of the second kind. Finally, several examples are presented to illustrate the application of the algorithm and results …