Good Textbook in Numerical PDEs?

Question

I am currently taking a course on Numerical PDE. The course covers the following topics listed below.

Chapter 1: Solutions to Partial Dierential Equations:

Chapter 2: Introduction to Finite Elements:

Answer 1

Numerical PDEs by J.W. Thomas might be a good book. If you check its table of contents, they have the majority of the topics you listed.

Here is one example of professor's lecture notes based on the same book.

Answer 2

A book I like, but I am probably biased since he was my professor is Dr. Jianke Yang's book Nonlinear Waves in Integrable and Non-integrable systems

It covers:

1. Derivation of non-linear waves
2. Integrable theory for the non-linear Schrodinger equation
3. Theories for integrable equations with order scattering operators
4. Soliton perturbation theory and applications
5. Theories for non-integrable systems
6. Nonlinear waves phenomena in periodic media
7. Numerical methods for non-linear wave equations

Also, Matlab code is provided in the book.

Answer 3

If any one tell me the basic and easy book with examples to understand the course of Numerical methods of PDE's. Contents are given: Boundary and initial conditions, Polynomial approximations in higher dimensions. Finite Difference Method: Finite Difference approximation. Finite Element Method: The Galerkin method in one and more dimension, Error bound on the Galarkin method, The Method of Collocation, Error bounds on the Collocation method, Comparison of efficiency of the finite difference and finite element method. Application to the solution of Linear and non-linear Partial Differential Equations appearing in Physical and engineering Problems.