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This textbook is written for senior undergraduate and gra- duate students as well as engineers who will develop or use code in the simulation of fluid flows or other physical phenomena. The objective of the book is to give the reader the basis for understanding the way numerical schemes achieve accurate and stable simulations of physical phenomena. It is based on the finite-difference method that allows also the analytic study of the problems. ODEs, hyperbolic, elliptic and parabolic types as well PDEs of the equations are treated. The reader will also find a chapter on the techniques of linearization of nonlinear problems. The final chapter applies the material to the equations of gas dynamics. The book builds on simple model equations and, pedagogically, on a host of problems given together with their solutions.
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