Finite Difference Methods in \(\mathbb {R}^1\)

  • David F. GriffithsEmail author
  • John W. Dold
  • David J. Silvester
Part of the Springer Undergraduate Mathematics Series book series (SUMS)


This chapter is an introduction to finite difference approximation methods. Key concepts like local truncation error, numerical stability and convergence of approximate solutions are developed in a one-dimensional setting. This chapter establishes the theoretical framework that is used to analyse the convergence of finite difference approximations in later chapters.


Local Truncation Error Fourth-order Finite Difference Method Inverse Monotone Suitable Comparison Function Second-order Consistency 
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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • David F. Griffiths
    • 1
    Email author
  • John W. Dold
    • 2
  • David J. Silvester
    • 2
  1. 1.University of DundeeFifeUK
  2. 2.School of MathematicsThe University of ManchesterManchesterUK

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