A Proposed Model to Modify the Newton- Raphson Method in Analyzing Ventilation Networks

Designing of ventilation networks is known a manual and computerized methods. Computerized method is carried out based on approximate mathematical approaches. Several approximate mathematical methods such as the Newton- Raphson, Hardy Cross and its corrected models, optimization techniques, critical path, linear and nonlinear methods can be used to design ventilation networks. One of the techniques for solving nonlinear equations in mathematical science is the Newton-Raphson method that is based on the derivative definition and its correction. This method is unable to produce valid results and also instead of convergence leads to divergence in some models. In addition, utilizing the Newton-Raphson method for analyzing of large-scale ventilation networks requires a lot of calculations. Therefore, in this paper a new method is presented naming Newton-Raphson method without derivatives. This new method is always convergent, capble to reduce mathematical calculations and it reaches to the result fast.