Description
Springer Introduction To Partial Differential Equations A Computational Approach 2004 Edition by Aslak Tveito Ragnar Winther
This book teaches basic methods of partial differential equations and introduces related important ideas associated with the analysis of numerical methods for those partial differential equations. Coverage details such topics as separation of variables Fourier analysis maximum principles and energy estimates. The book introduces numerical methods in parallel to the classical theory and also includes many engaging exercises. Table of contents : Setting the Scene.- Two-Point Boundary Value Problems.- The Heat Equation.- Finite Difference Schemes for the Heat Equation.- The Wave Equation.- Maximum Principles.- Poisson's Equation in Two Space Dimensions.- Orthogonality and General Fourier Series.- Convergence of Fourier Series.- The Heat Equation Revisited.- Reaction-Diffusion Equations.- Applications of the Fourier Transform.