Ordinary Differential Equations and the Approximation module (MA41003)

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Ordinary differential equations (ODEs) are an essential modelling tool in science and engineering. ODEs can rarely be solved exactly, and techniques have been developed to derive approximate solutions that may, in principle, be made as accurate as desired. In this module, you will learn the basic numerical methods for the approximate solution of initial and boundary value problems (IVPs and BVPs). You will engage with the construction of these methods and with aspects of consistency, stability and convergence theory, i.e. the fundamental properties that make the most successful methods stand out.  

Topics include:  

  • ODEs -- an introduction  
  • The Taylor series method     
  • Linear multistep methods (LMMs)   
  • Convergence and zero–stability of LMMs   
  • Absolute stability of LMMs   
  • Runge-Kutta methods   
  • Boundary value problems   
  • Comparison principles for BVPs   
  • Approximation of BVPs. 



This module is available on following courses: