This textbook deals with the numerical solution of initial and boundary value problems for ordinary differential equations. It takes the reader directly to the practically proven methods from their theoretical foundation via their analysis to questions of implementation. The textbook contains a wealth of exercises together with numerous application examples. Sections of this third edition have been revised and it has been supplemented with MATLAB codes.

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This book deals with the general topic "Numerical solution of partial differential equations (PDEs)" with a focus on adaptivity of discretizations in space and time. By and large, introductory textbooks like "Numerical Analysis in Modern Scientific Computing" by Deuflhard and Hohmann should suffice as a prerequisite. The emphasis lies on elliptic and parabolic systems. Hyperbolic conservation laws are treated only on an elementary level excluding turbulence.

Numerical Analysis is clearly understood as part of Scientific Computing. The focus is on the efficiency of algorithms, i.e....

Deals with the efficient numerical solution of challenging nonlinear problems in science and engineering, both in finite dimension (algebraic systems) and in infinite dimension (ordinary and partial differential equations). This title focuses on local and global Newton methods for direct problems or Gauss-Newton methods for inverse problems.