Choosing a book for learning about PDEs numerical methods can be overwhelming due to the vast amount of resources available. It is important to consider your level of mathematical background, your specific interests in PDEs, and the level of detail you are looking for in a book. It may be helpful to read reviews and ask for recommendations from other scientists or professors in the field.
For beginners, some recommended books are "A First Course in Numerical Methods for Differential Equations" by Arieh Iserles, "Numerical Methods for Partial Differential Equations" by George F. Pinder, and "An Introduction to Partial Differential Equations" by Yehuda Pinchover and Jacob Rubinstein. These books provide a solid foundation in PDEs numerical methods and are suitable for those with limited mathematical background.
Yes, there are books that focus on specific types of PDEs numerical methods, such as "Finite Difference Methods for Ordinary and Partial Differential Equations" by Randall J. LeVeque, which covers finite difference methods for both ODEs and PDEs, and "Finite Element Methods for Partial Differential Equations" by Claes Johnson, which focuses on finite element methods for PDEs.
For those looking for more advanced material, "Numerical Solution of Partial Differential Equations: Finite Difference Methods" by G. D. Smith and "Numerical Methods for Partial Differential Equations: Finite Difference and Finite Volume Methods" by Sandip Mazumder are excellent choices. These books cover a wide range of advanced topics and are suitable for graduate level students and researchers.
Yes, there are many online resources available for learning about PDEs numerical methods. Some recommended websites are MIT OpenCourseWare, which offers free online courses on various topics, including PDEs numerical methods, and the Numerical PDEs website, which provides lecture notes, software, and other resources for learning about numerical methods for PDEs.