I prefer a method to obtain a close form solution of volterra integral equation of second kind with non linear kernel. But if such method doesn't exist, any method will be of help.
Hello Mr. Oseni,
i am not an expert in this field, however, a way of solving ordinary differential equations are linearization methods. In Martinez-Gaza (2010) a solution with a quasi-linearization method is described for volterra integrals of the second kind. This article is accessible via google search. Additionally, in this article are several cites on this topic which may help you diving into this topic.
Greetings from Germany,
Patrick
*Martinez-Gaza (2010), "Newton-type Schemes via the Method of Generalized
Quasilinearization for Volterra Integral Equations of the Second Kind", Journal of Mathematics Research, Vol. 2, Nr. 3, pp. 3-11.
http://ccsenet.org/journal/index.php/jmr/article/viewFile/4899/5356
Run MATLAB Demo file which utilizes ODE (Ordinary Differential Equations solvers Runge - Kutta 23 or 45); it is easy to find out how to generalize it for more complicated equations.
If the kernel have some particular form, then its possible to obtain a close form of solution for Volterra integral equation of second type.
In the general case such a method does not exist.
Thanks every one. Prof. Patrick am looking at the paper presently, It seems the paper describes numerical method.
Prof. Shakouri, thanks for the idea.
Prof. Anton, I have not come across my kernel in any literature yet. Probably the close form method does not exist. Thanks so much.
- Badges
- Science topic
- Similar topics
- Mathematical Sciences
- Graphs