Newton-Raphson Root Finding, Difficulty in coding
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- Subject: [mg131809] Newton-Raphson Root Finding, Difficulty in coding
- From: Cory <leahyc1 at apps.tcnj.edu>
- Date: Wed, 9 Oct 2013 02:11:59 -0400 (EDT)
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Hello I need to use the Newton Raphson Method to find values of Specific Volume from the Van der Waal equation over a process of constant Temperature but variant Pressure. I've worked Mathematica to be able to spit out a list of however many iterations I want between the desired Pressure min and max (3.9 atm to 59.2 atm). Further, I am able to find the root of a single specified element in the list. However, I am unable to figure out how to get the roots (Specific volumes) for all elements at once. For example: ---------------------------------------------------------- FindRoot[v[[59]] == 0, {vi, 4}, WorkingPrecision -> 20] ---------------------------------------------------------- will show vi, specific volume, for the 59th element in the list. I've tried the following, thinking this would work for multiple elements: ---------------------------------------------------------- FindRoot[v[[1;;60]] == 0, {vi, 4}, WorkingPrecision -> 20] ---------------------------------------------------------- However I receive an error. "FindRoot::nveq: "The number of equations does not match the number of variables in FindRoot[v[[1;;60]]==0,{vi,4},WorkingPrecision->20]."" This is my code: ---------------------------------------------------------- a = 1.36; b = .003183; R = .0820578; T = 333; inc = (59.2 - 3.9)/60; v = Table[ vi - ((((atm) + (a/vi^2)) (vi - b) - (R*T))/((atm) - (a/ vi^2) + (2 a*b/vi^3))), {atm, 3.9, 59.2, inc}] FindRoot[v[[59]] == 0, {vi, 4}, WorkingPrecision -> 20] --------------------------------------------------------- Any help would be greatly appreciated! Thanks
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