Titlebook: Numerical Methods for Initial Value Problems in Physics; Francisco S. Guzmán Textbook 2023 The Editor(s) (if applicable) and The Author(s)

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Ordinary Differential Equations,g of nonlinear coupled equations. Error estimates of numerical solutions, as well as convergence and self-convergence tests are essential to our approach, and their implementation is described in detail. In the final section, we present a number of applications that range from purely dynamical systems to problems of celestial mechanics.

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lved problems, exercises, and projects.This textbook is a comprehensive overview of the construction, implementation, and application of important numerical methods for the solution of Initial Value Problems (IVPs). Beginning with IVPs involving Ordinary Differential Equations (ODEs) and progressing

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Initial Value Problems in 3+1 and 2+1 Dimensions, leave the reader in a position from which it will be possible to tackle state-of-the-art problems. The three representative problems in three spatial dimensions involve the wave equation, Schrödinger equation, and Euler equations. At the end of the chapter, we present examples with the 2+1 diffusion equation.

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978-3-031-33558-7The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Appendix B: Codes,The codes that reproduce the results in this book are available as Electronic Supplementary Material (ESM). In the first section of this appendix, we describe the list of codes in the ESM used to reproduce the results of each chapter, written both in Fortran 90 and C++.

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Francisco S. GuzmánCovers a wide range of numerical methods and applications.Provides code in Fortran and C++ for readers to implement.Each chapter contains solved problems, exercises, and projects

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Simple Methods for Initial Value Problems Involving PDEs,mple and implicit schemes in the solution of the Diffusion equation. We finish the chapter with the solution of Schrödinger equation. In this chapter, the specific IVPs studied are the paradigms of hyperbolic, parabolic, and complex equations.