Comparison of Eulers method with exact solution

Comparison of Euler s method with exact solution 

The general approach to solving stiff equations is to use implicit methods. Historically, two chemical engineers, Curtis and Hirschfelder ([11]), proposed the first set of numerical formulas that are well-suited for stiff initial value problems by adopting  

Both schemes are implicit and belong to the well-known class of backward difference formula (BDF), the first one being the implicit Euler s scheme. 

Consider the same differential equation presented earlier (Equation 2.15), and apply a backward Euler s method, which leads to the following solution. 

A detailed theory of stability and the different definitions of stability criteria (e.g., A-stable systems, stiffly stable systems, etc.) are beyond the scope of this book and readers are advised to look elsewhere for details ([9, 12, 13, 14, 15]). There are large numbers of stiff algorithms derived based 

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