References for linear advection system with constant coefficients

Question

I'm searching for references where I can found the study of finite difference schemes for linear advection system with constant coefficients. More specifically, I would like to read about: The Symbol, Phase and Amplitude Errors, dissipation and dispersion, and some MATLAB examples

Thanks you a lot for your help

Answer 1

You might be interested by Chap. 3 of the book [1]:

3 Finite Difference Methods for Hyperbolic Equations

3.1 Introduction 3.2 Some basic difference schemes 3.3 Dissipation and dispersion errors 3.4 Extensions to conservation laws 3.5 The second-order hyperbolic PDEs 3.6 Numerical examples with MATLAB codes 3.7 Bibliographical remarks 3.8 Exercises

Besides the absence of Matlab examples, you might also enjoy Chap. 5 of the monograph [2] which includes many exercises & detailed examples.

[1] J. Li, Y.-T. Chen: Computational Partial Differential Equations Using MATLAB®, 2nd ed., Chapman & Hall/CRC, 2020.

[2] J.C. Strikwerda: Finite Difference Schemes and Partial Differential Equations, 2nd ed., SIAM, 2004.