Problem Statement: Write a program to find a solution to the following set of algebraic equations.

     sin(x) + y2 + ln(z) = 7
     3x + 2y + 1 = z3
     x + y + z = 5

Solution:

• Answer: x = 0.5990, y = 2.396, z = 2.005.
• FORTRAN (Call MNEWT of NR)
  • FORTRAN Source Code (newton4.for)
  • Executable Program (newton4.exe)
• FORTRAN, with the Levenberg-Marquardt Algorithm, no Jacobian (Call NEQNF of IMSL)
  • FORTRAN Source Code (newton5.for)
  • Executable Program (newton5.exe)
• FORTRAN, no Jacobian (Call NEWTND of Riggs -- presented as a lesson, not recommended)
  • FORTRAN Source Code (newton6.for)
  • Executable Program (newton6.exe)
• QBasic (Call MNEWT of NR)
  • QBasic Source Code (newton4b.bas)
  • Executable Program (newton4b.exe)
• QBasic (Call MNEWT of NR, approximate Jacobian)
  • QBasic Source Code (newton5b.bas)
  • Executable Program (newton5b.exe)
• MATLAB /w "fsolve"
  • Main M-Script File (newton5.m)
  • f(x)=0 Function (myfxeq05.m)
  • The following MATLAB functions are all needed for "fsolve": fsolve.m, fsolve2.m, leastsq.m, lsint.m, quadi.m, searchq.m, cubici1.m, cubici2.m, cubici3.m.
• Mathcad
  • Snapshot of Mathcad Screen (eqn.gif)
  • Mathcad File (eqn.mcd)
• Excel (Call MNEWT of NR)
  • Snapshot of Spreadsheet Screen (eqnx.gif)
  • Excel File (eqnx.xls)
  • Visual Basic Module (eqnx.bas)

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Computer Methods in Chemical Engineering -- Multi-Dimensional Nonlinear Algebraic Equations
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Nam Sun Wang Department of Chemical & Biomolecular Engineering University of Maryland College Park, MD 20742-2111 301-405-1910 (voice) 301-314-9126 (FAX) e-mail: nsw@umd.edu ©1996-2006 by Nam Sun Wang