A First Course in the Numerical Analysis of Differential Equations

Numerical Analysis Presents Different Faces To The World. For Mathematicians It Is A Bona Fide Mathematical Theory With An Applicable Flavour. For Scientists And Engineers It Is A Practical Applied Subject Part Of The Standard Repertoire Of Modelling Techniques. For Computer Scientists It Is A Theory On The Interplay Of Computer Architecture And Algorithms For Real-Number Calculations. The Tension Between These Standpoints Is The Driving Force Of This Book Which Presents A Rigorous Account Of The Fundamentals Of Numerical Analysis Of Both Ordinary And Partial Differential Equations. The Exposition Maintains A Balance Between Theoretical Algorithmic And Applied Aspects. This Second Edition Has Been Extensively Updated And Includes New Chapters On Emerging Subject Areas: Geometric Numerical Integration Spectral Methods And Conjugate Gradients. Other Topics Covered Include Multistep And Runge-Kutta Methods; Finite Difference And Finite Elements Techniques For The Poisson Equation; And A Variety Of Algorithms To Solve Large Sparse Algebraic Systems.