Numerical Solution of Ordinary Differential Equations

In this chapter we deal with the numerical solutions of the Cauchy problem for ordinary differential equations (henceforth abbreviated by ODEs). After a brief review of basic notions about ODEs, we introduce the most widely used techniques for the numerical approximation of scalar equations. The concepts of consistency, convergence, zero-stability and absolute stability will be addressed. Then, we extend our analysis to systems of ODEs, with emphasis on stiff problems.KeywordsAbsolute StabilityMultistep MethodLocal Truncation ErrorLinear Multistep MethodRoot ConditionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning…