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I would like to get to know more in details about Lax-Richtmyer stability analysis (esp in examples), but I didn't manage to find anything except a definition. Could you advice any sources for this subject?

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You could always read the paper. But my favorite explanation is in Chapter 9 of LeVeque's finite difference book. It includes examples proving stability of several discretizations. Most introductory textbooks on numerical methods for PDEs will cover this.

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You can try to read this: http://arxiv.org/abs/math/0507288 and the references mentioned in the paper.

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    $\begingroup$ Hi @StudioseLudi and welcome to scicomp! Instead of just posting a link, it would be helpful to summarize why you recommend this paper and how it addresses the OP's question. Also, since links change over time, it's better to provide the full name of the article as well as the link. $\endgroup$
    – Paul
    Commented Sep 11, 2014 at 17:44
  • $\begingroup$ Thanks, @Studiose Ludi, this information is useful, but does not refer to the subject of question in proper degree $\endgroup$
    – cool
    Commented Sep 11, 2014 at 18:06

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