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Convergence of Numerical Methods

Chapter 2 Convergence of Numerical MethodsIn the last chapter we derived the forward Euler method from aTaylor series expansion ofun+1and we utilizedthe method on some simple example problems without any supporting analysis. This chapter onconvergencewillintroduce our first analysis tool in Numerical Methods for the solution of Self-AssessmentBeforereading this chapter, you may wish to limits [ Lecture 2: Video]Afterreading this chapter you should be able list the two primary sources of error in the Numerical solution of ODEs describe the concept of Convergence of a Numerical method discuss the relationship between global order of accuracyand the rate of Convergence of a Numerical method evaluate the global order of accuracy of a method from experimental data7 Types of errors in the Numerical solution of ODEsWhen we approximate the solution of ODEs numerically, there are two primary sources of error: rounding (or floatingpoi)

Convergence of Numerical Methods In the last chapter we derived the forward Euler method from a Taylor series expansion of un+1 and we utilized the method on some simple example problems without any supporting analysis. This chapter on convergence will introduce our first analysis tool in numerical methods for th e solution of ODEs. 6 Self ...

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