A Mathematica Program for the Newton Raphson Method

The following Mathematica program implements the widely used Newton Raphson approach. Any functions may be considered here, and the following program is ready to evaluate it.

(*Mathematica Codes for Newton-Raphson Approach*)

(*Write Your Own Function Below*)

Sigma = 100000*(Sqrt[epsilon] + 1/80*Sin[Pi*epsilon/0.002]) - 4000;

SigmaDerivative = D[Sigma, epsilon];

epsilontable = {0.0002};

Error = {1};

SetTolerance = 0.0005;

MaximumIteration = 100;

i = 1;

(*Newton-Raphson Algorithm Implementation*)

While[And[i <= MaximumIteration, Abs[Error[[i]]] > SetTolerance],

  epsilonnew = 

   epsilontable[[i]] - (Sigma /. 

       epsilon -> epsilontable[[i]])/(SigmaDerivative /. 

       epsilon -> epsilontable[[i]]); 

  epsilontable = Append[epsilontable, epsilonnew]; 

  Errornew = (epsilonnew - epsilontable[[i]])/epsilonnew; 

  Error = Append[Error, Errornew];

  i++];

L = Length[epsilontable];

SolutionTable = 

  Table[{i - 1, epsilontable[[i]], Error[[i]]}, {i, 1, L}];

SolutionTable1 = {"Iteration Number", "Epsilon", "Error"};

L = Prepend[SolutionTable, SolutionTable1];

Print["Showing Results for the Newton-Raphson Approach when Sigma is \

4,000 and Initial Guess is 0.0002"]

ScientificForm[L // MatrixForm, 4]

Program Output: