Could you please give me some references about the history of difference equations.
Thank you for your reply
This is a difficult question to answer, but an excellent question nonetheless. This answer is offered presuming an interest regarding the inception and historical development of difference equations. As one becomes aware in researching such an history, greater interest was given in the application of the methods but not so much in their history and development. This was probably due largely by the isolation of individuals from others of similar interests, except within their own academic community, such as at a university. Outside communication was by letter, or by travel to scientific meetings. Nevertheless, people compiled their notes into books, treatises, and pamphlets, which were given to students, sold to individuals, or distributed to libraries at other universities. People read these books, took note of the methods, but other than to put a person's name to the method, passed by the historical development. Consequently, when one looks for historical notes in a book, little more is found than a citation to an essential or original text documenting the method in its first instance. Books in analysis abound with exactly these citations, but little historical commentary.
One book, however, has a few very brief historical notes regarding exactly the historical development of difference equations -
Charles Jordan, Calculus of Finite Differences. 2nd Ed., 1950 (reprinted 1960). Chelsea Publishing Company, New York. 652 pp.
Pay particular attention to the author's preface, and further comments in Chapter 1, Section 1, Historical and Bibliographical Notes, p. 1 ff. Note that when Jordan is discussing the Computer or Computers, he is referencing human computation by hand. The book is rich with bibliographic notes and comments in the text, but the text is primarily about methods and applications in numerical analysis. The book is available electronically here. Perhaps you have already seen this book.